DIGIMAT is an advanced HTML-5 based Video Learning Platform for Streaming 70,000+ HD Quality NPTEL Video Lectures in Smart Devices. He is currently a National MOOCs Coordinator for NPTEL in the SWAYAM project of the MHRD. Topic(s) Linear Algebra ; Take course. Algebra 2 Delivered by Other. Linear Algebra – K Hoffman, R Kunze ... photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur. What comes after calculus? It's definitely even more abstract than calculus. 2. This section contains a complete set of video lectures on linear algebra along with transcripts and related resource files. Linear dependence and independence, Bases and Dimensions – I, Bases and Dimension - II, Linear Transformation - I, Orthogonal subspaces, Row space, column space and null Space, Eigenvalues and Eigenvectors-I, Eigenvalues and, Orthogonal Sets, Gram Schmidt orthogonalization and orthonormal bases, Introduction to Matlab, Sign integer representation, Floating point representation, Round-off error, Error propagation in computer arithmetic, Addition and multiplication of floating, Conditioning and condition numbers-II, Stability of numerical algorithms-I, Stability of numerical algorithms-II, Vector, Estimation of the condition number,  Singular value decomposition of a matrix – I, Singular value decomposition of a, : SVD and their applications, Perturbation theorem for singular values, Outer product expansion of a matrix, Least. Please choose the SWAYAM National Coordinator for support. Only the e-certificate will be made available. Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course. Mathematics in India - From Vedic Period to Modern Times. The online registration form has to be filled and the certification exam fee needs to be paid. Mathematics - II Mathematics - II. 111101003. Prof. From Geometry to Algebra, an introduction to linear Algebra, Inder K Rana, Ane Books 2007. IIT Madras, Linear Algebra Done Right - Sheldon Axler, Introduction to Linear Algebra - Gilbert Strang, Linear Algebra and Applications - Gilbert Strang, Linear Algebra, S.H. FREE. $1,880+ Pace. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in His area of research includes approximation Theory and Complex Analysis. Search by NPTEL Course ID, Course Name, Lecture Title, Coordinator. Insel, and L.E. Before joining IIT Roorkee, he worked as a faculty member in BITS-Pilani Goa campus and LNMIIT Jaipur. 111101005. Lecture notes on linear algebra by David Lerner Department of Mathematics University of Kansas and The students of Math 291 (Fall, 2007) These are notes of a course given in Fall, 2007 to the Honors section of our elementary linear algebra course. COURSES >> NPTEL >> Mathematics >> Linear Algebra Author Dr. Wagish Shukla,Dr. INSTRUCTOR BIO. Gupta of the same department. Please choose the SWAYAM National Coordinator for support. 2. He has already prepared e-notes for the course titled “Ordinary Differential Equations and Special Functions” under e-Pathshala funded by UGC. Friedberg, A.J. Hard copies will not be dispatched. In this regard, we would like to have a feedback from you regarding our course and whether there are any improvements, you would like to suggest. Prof. Andrew Thangaraj IIT Madras. Happy learning. Andrew Thangaraj received his B.Tech in Electrical Engineering from the Indian Institute of Technology (IIT), Madras, India in 1998 and a PhD in Electrical Engineering from the Georgia Institute of Technology, Atlanta, USA in 2003. Lecture 1 is in three parts: part a, part b, and part c. First homework Solutions to first homework. Senior level Undergraduate and First year Postgraduate/PhD, Basic Calculus, Should have done a basic (or a first) course in Linear Algebra, Communications, Artificial Intelligence, Analytics. Lecture 3. Lecture Series on Mathematics - II by Dr.Sunita Gakkhar, Department of Mathematics, IIT Roorkee. NPTEL Online Videos, Courses - IIT Video Lectures Well Organized! From Geometry to Algebra, an introduction to linear Algebra, Inder K Rana, Ane Books 2007. Prof. Linear Algebra, S.H. 111101003. Since Oct 2011, he has been serving as NPTEL coordinator at IIT Madras. William Ford, Numerical Linear Algebra with Applications, Academic Press, 2014.. INSTRUCTOR BIO. NPTEL NPTEL ONLINE CERTIFICATION COURSE Linear Algebra Tutorial CS5011 – Machine Learning Abhinav Garlapati Varun Gangal Department of Computer Science IIT Madras January 17, 2016 Hi everyone welcome to the second tutorial of the introduction to machine learning course. V. Sundarapandian, Numerical Linear Algebra, PHI, 2008. These videos are provided by NPTEL e-learning initiative. NPTEL provides E-learning through online Web and Video courses various streams. Now we use determinants and linear algebra. 4. Applications of linear algebra 1. Numerical Linear Algebra.Instructors: Dr. P. N. Agrawal and Dr. D. N. Pandey, Department of Mathematics, IIT Roorkee. The matrix A I times the eigenvector x is the zero vector. Exam score = 75% of the proctored certification exam score out of 100, Final score = Average assignment score + Exam score, Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at. Hard copies will not be dispatched. MATHEMATICS. These Engineering Mathematics (Math) Study notes will help you to get conceptual deeply knowledge about it.We are here to provides you the Best Study Notes from Best coachings like Made easy, ACE academy etc.. and Lecture notes from best institutions like MIT (Open Course), IIT (NPTEL) & TuDelft Open Courses and VSSUT, VIT, ETH Zurich, Texas A&M, Texas Rio Grande Valley, Cambridge, … Search by NPTEL Course ID, Course Name, Lecture Title, Coordinator. Spence. These linear algebra lecture notes are designed to be presented as twenty ve, fty minute lectures suitable for sophomores likely to use the material for applications but still requiring a solid foundation in this fundamental branch of mathematics. HOME. Write the equation Ax D x as .A I/ x D 0. From June 2004, he has been with the Department of Electrical Engineering, IIT Madras, where he is currently a professor. So in this tutorial we shall be taking a tour of the aspects of linear algebra which you would need for the course. For more details on NPTEL visit http://nptel.iitm.ac.in. Okay I clearly care too much about teaching linear algebra: I. 111108066. Spence. I am Emeritus Fellow at Department of Mathematics, IIT Bombay. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Currently, he is supervising five research students. Abstractly, it is the study of vector spaces over fields, and their linear maps and bilinear forms. He is currently a National MOOCs Coordinator for NPTEL in the SWAYAM project of the MHRD. Linear algebra! Linear Algebra and its Applications – Gilbert Strang, Cenage Learning. The eigenvectors make up the nullspace of A I . Only the e-certificate will be made available. Linear Algebra 7. … His area of expertise includes semigroup theory and functional differential equations of fractional and integral orders. First move x to the left side. Biswa Nath Dutta, Numerical Linear Algebra and Applications, SIAM, 2010. Happy learning. 2. Numerical Linear Algebra. Elementary Numerical Analysis. Elementary Numerical Analysis . It is essential for the students to get acquainted with the subject of Abstract and Linear Algebra at an early stage. We will then go into functions from one vector space to another, commonly known as linear transformations. NPTEL provides E-learning through online Web and Video courses various streams. More details will be made available when the exam registration form is published. Also, he has published a book titled “Nonlocal Functional Evolution Equations: Integral and fractional orders, LAP LAMBERT Academic Publishing AG Germany”. Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc. He has guided three PhD theses and has published more than 60 papers in various international journals of repute. Linear Equations; 3a. Insel, and L.E. NPTEL NPTEL ONLINE CERTIFICATION COURSE Linear Algebra Tutorial CS5011 – Machine Learning Abhinav Garlapati Varun Gangal Department of Computer Science IIT Madras January 17, 2016 Hi everyone welcome to the second tutorial of this of the introduction to machine learning course, so in this tutorial we shall be taking a tour of the aspects of linear algebra which you Advanced Matrix Theory and Linear Algebra for Engineers by Prof. Vittal Rao ,Centre For Electronics Design and Technology, IISC Bangalore. Introduce the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students. Mathematics. We shall mostly be concerned with matrices having real numbers as entries. : Psudeo - inverse  and least square solution, Householder  matrices  and their applications, Householder QR factorization –I. I have taught couses at B.Tech, M.Sc., and Ph.D level for the last 34 years. Sivakumar from IIT Madras.Click on any Lecture link to view that video. Lecture 2. If there are any changes, it will be mentioned then. 1. Linear Algebra. Some lecture notes I once prepared on this material may be found here (Note: These talks can be viewed most easily with a VLC player.) These videos are provided by NPTEL e-learning initiative. Register by. This is the first in a series of lectures for a college-level linear algebra course. Mathematics for Finance and Actuarial Studies 2 Delivered by Other. Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm. Linear Equations: 3. Click on any Lecture link to view that video. Dr. D. N. Pandey is an Associate Professor in the Department of Mathematics, IIT Roorkee. These linear algebra lecture notes are designed to be presented as twenty ve, fty minute lectures suitable for sophomores likely to use the material for applications but still requiring a solid foundation in this fundamental branch of mathematics. Instructor-led. This is the first in a series of lectures for a college-level linear algebra course. INSTRUCTOR BIO. Ordinary Differential Equations and Applications. Exam score = 75% of the proctored certification exam score out of 100, Final score = Average assignment score + Exam score, Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee.It will be e-verifiable at. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit httpnptel.ac.in. Subject. HOME. Linear Algebra by Dr. K.C. The main idea of the course is to emphasize the concepts NOC:Basic Calculus for Engineers, Scientists and Economists. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, image processing, numerical analysis and dynamical systems etc. 111101080. Introduction to the Course Contents. Course language. The exam is optional for a fee of Rs 1000/- (Rupees one thousand only). More details will be made available when the exam registration form is published. Abstractly, it is the study of vector spaces over fields, and their linear maps and bilinear forms. He has played a key role in initiating and running NPTEL online courses and certification. Friedberg, A.J. He taught the course on “Integral equations and calculus of variations” several times to MSc (Industrial Mathematics and Informatics) students. Related Courses. Toggle … Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur .It will be e-verifiable at nptel.ac.in/noc. Friedberg, A.J. Linear Algebra. COURSE CERTIFICATE The course is free to enroll and learn from. Linear Algebra - (Mathematics course from IIT Madras) NPTEL Lecture Videos by Dr. K.C. Numerical Linear Algebra.Instructors: Dr. P. N. Agrawal and Dr. D. N. Pandey, Department of Mathematics, IIT Roorkee. Numerical Linear Algebra https://onlinecourses.nptel.ac.in/noc18_ma01/preview Measure and Integration. It contains basics of matrix algebra, computer arithmetic, conditioning and condition number, stability of numerical algorithms, vector and matrix norms, convergent matrices, stability of non-linear systems, sensitivity analysis, singular value decomposition (SVD), algebraic and geometric properties of SVD, least square solutions, Householder matrices and applications, QR method, Power method and applications, … Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc. 2. 10 Rockafeller-Pshenichny optimality condition 11 Properties of normals & projections 12 Computing the normal cone of inequality constraints. Course description. Second homework Solutions to second homework. 111108081. The aim of this course is to take a beginning student, with some prior exposure to elementary transform and linear algebra, through a motivated and integrated development of the fuller perspective of the linear system theory. Chapter 1 Matrices 1.1 Definition of a Matrix Definition 1.1.1 (Matrix) A rectangular array of numbers is called a matrix. * : By Prof. Andrew Thangaraj   |   Lecture 3. If there are any changes, it will be mentioned then. He has played a key role in initiating and running NPTEL online courses and certification. HOME. Lecture 1 is in three parts: part a, part b, and part c. First homework Solutions to first homework. However, it is important to note that nearly all arguments in Linear Algebra use only the axioms for a eld and so are valid for any eld, which is why shall use a general eld Kfor most of the course. From here, we will go into the axiomatic definition of vector spaces over real and complex numbers, try to understand linear combination, linear span, linear independence and linear dependence and hopefully understand the basis of a finite dimensional vector space. Mathematics - Advanced Matrix Theory and Linear Algebra for Engineers Addeddate 2019-06-02 22:31:15 Identifier NPTEL-Math-Advanced_Matrix_Theory_and_Linear_Al Ocr ABBYY FineReader 11.0 (Extended OCR) Ppi 300. plus-circle Add Review. NPTEL provides E-learning through online Web and Video courses various streams. Lecture 1 - Matrix Operations and Types of Matrices. His area of research includes approximation Theory and Complex Analysis. NPTEL provides E-learning through online Web and Video courses various streams. Linear Algebra and its Applications, 5th edition, by David C. Lay, Steven R. Lay, and Judi J. McDonald. Spence. Registration url: Announcements will be made when the registration form is open for registrations. Linear algebra has two aspects. Prof. P. N. Agarwal IIT Roorkee . Second homework Solutions to second homework. He was a post-doctoral researcher at the GTL-CNRS Telecom lab at Georgia Tech Lorraine, Metz, France from August 2003 to May 2004. List of Topics. He has supervised nine Ph.D. theses and has published more than 187 research papers in reputed international journals of the world. Once again, thanks for your interest in our online courses and certification. Abstract and Linear Algebraare applicable to every discipline, be it engineering and technology, economics or social sciences. He has delivered several invited talks at reputed institutions in India and abroad. IIT Roorkee. This is the key calculation in the chapter—almost every application starts by solving Ax D x. Take course. 15 . 3. January 21, 2021. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in Registration url: Announcements will be made when the registration form is open for registrations. The horizontal arrays of a matrix are called its rowsand the vertical arrays are called its columns. NPTEL Video Course : NOC:Numerical Linear Algebra Lecture 1 - Matrix Operations and Types of Matrices Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge University Press, 1994. ... Advanced Matrix Theory and Linear Algebra for Engineers. Degree Credit. This course is a basic course offered to UG/PG students of Engineering/Science background. Linear Algebra. It will be e-verifiable at nptel.ac.in/noc • Only the e-certificate will be made available. We hope you found the NPTEL Online course useful and have started using NPTEL extensively. I. K. Rana IIT Bombay. NPTEL NPTEL ONLINE CERTIFICATION COURSE Linear Algebra Tutorial CS5011 – Machine Learning Abhinav Garlapati Varun Gangal Department of Computer Science IIT Madras January 17, 2016 Hi everyone welcome to the second tutorial of the introduction to machine learning course. This course is a basic course offered to UG/PG students of Engineering/Science background. Calculus of Sub differentials NPTEL Mathematics Pre-requisites: Knowledge in Linear Algebra & Real Analysis Hyperlinks: Stephen Byod lectures on Convex Optimization Coordinators: Dr. Joydeep Dutta IIT Kanpur. Abstract and Linear Algebraare applicable to every discipline, be it engineering and technology, economics or social sciences. Linear system is the cornerstone of control theory and a prerequisite subject for almost all advanced level graduate courses in this area. Further he has completed online certification course “Mathematical methods and its applications” jointly with Dr. S.K. Intermediate. * : By Prof. P. N. Agarwal, Prof. D. N. Pandey   |   Concretely, it is matrix theory: matrices occur in all parts of mathematics and its applications, and everyone work-ing in the mathematical sciences and related areas needs to … Introduction to the Course Contents. We hope you found the NPTEL Online course useful and have started using NPTEL extensively. INSTRUCTOR BIO. William Ford, Numerical Linear Algebra with Applications, Academic Press, 2014.. Dr. P. N. Agarwal is a Professor in the Department of Mathematics, IIT Roorkee. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay.It will be e-verifiable at nptel.ac.in/noc. Linear Algebra, S.H. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course. NPTEL Video Lectures, IIT Video Lectures Online, NPTEL Youtube Lectures, Free Video Lectures, NPTEL Online Courses, Youtube IIT Videos NPTEL Courses. It is essential for the students to get acquainted with the subject of Abstract and Linear Algebra at an early stage. The exam is optional for a fee of Rs 1000/- (Rupees one thousand only). Sivakumar from IIT Madras "Linear Algebra" - Video Lectures 1. Sivakumar from IIT Madras. Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm. I. K. Rana IIT Bombay. Learn various topics within linear algebra. Lecture notes on linear algebra by David Lerner Department of Mathematics University of Kansas and The students of Math 291 (Fall, 2007) These are notes of a course given in Fall, 2007 to the Honors section of our elementary linear algebra course. Andrew Thangaraj received his B.Tech in Electrical Engineering from the Indian Institute of Technology (IIT), Madras, India in 1998 and a PhD in Electrical Engineering from the Georgia Institute of Technology, Atlanta, USA in 2003. Linear Algebra - (Mathematics course from IIT Madras) NPTEL Lecture Videos by Dr. K.C. Upon successful completion of the course, students will be able to demonstrate mastery over the following topics: Linear Equations in Linear Algebra. SYSTEMS OF LINEAR EQUATIONS. In some ways it's easier, but in other ways it's harder. Lecture 2. But if you want a certificate, you have to … Some lecture notes I once prepared on this material may be found here (Note: These talks can be viewed most easily with a VLC player.) English; Difficulty. The online registration form has to be filled and the certification exam fee needs to be paid. English; Video Transcript. Feedback for Numerical Linear Algebra Dear student We are glad that you have attended the NPTEL online certification course. Since Oct 2011, he has been serving as NPTEL coordinator at IIT Madras. Once again, thanks for your interest in our online courses and certification. It contains basics of matrix algebra, computer arithmetic, conditioning and condition number, stability of numerical algorithms, vector and matrix norms, convergent matrices, stability of non-linear systems, sensitivity analysis, singular value decomposition (SVD), algebraic and geometric properties of SVD, least square solutions, Householder matrices and applications, QR method, Power method and applications, Jacobi method for finding the eigenvalues of a given matrix. Linear algebra has two aspects. The lectures were distributed to the students before class, then posted on a 1. Currently, he is supervising eight research students. Toggle navigation. ISBN 13: 978-0-321-98238-4. So in this tutorial we shall be taking a tour of the aspects of linear algebra which you would need for the course. Numerical Linear Algebra. 1. Feedback for Numerical Linear Algebra Dear student We are glad that you have attended the NPTEL online certification course. Equivalent Systems of Linear … Credit. Linear Algebra by Dr. K.C. MATHEMATICS. Measure and Integration. Linear Algebra by Dr. K.C. Lec : 1; Modules / Lectures . Advanced Matrix Theory and Linear Algebra for Engineers by Prof. Vittal Rao ,Centre For Electronics Design and Technology, IISC Bangalore. This course is a basic course offered to UG/PG students of Engineering/Science background. Since Jan 2012, he has been serving as Editor for the IEEE Transactions on Communications. Harvard Extension School. Insel, and L.E. Linear Transformation, Rank-Nullity Theorem, Row and column space: PDF Lecture 11 Rank of a matrix, solvability of system of linear equations, examples: PDF: Lecture 12 Some applications (Lagrange interpolation, Wronskian), Inner product: PDF: Lecture 13 Orthogonal basis, Gram-Schmidt process, orthogonal projection: PDF: Lecture 14 : basic calculus for Engineers by Prof. Vittal Rao, Centre for Electronics Design and,... Prepared e-notes for the students to get acquainted with the subject of Abstract and Linear Algebra and Applications!, SIAM, 2010 for registrations changes, it will be mentioned then inner products Linear! Other ways it 's easier, but in other ways it 's harder Rockafeller-Pshenichny..., Coordinator for Engineers, Scientists and Economists one vector space to another, commonly as! For Numerical Linear Algebra for Engineers, Householder QR factorization –I the make... Eigenvector x is the zero vector 12 Computing the normal cone of inequality constraints numbers is called Matrix... For almost all advanced level graduate courses in this tutorial we shall mostly be concerned with matrices having real as... Dr. K.C Linear transformations http: //nptel.ac.in Linear Algebra Dear student we are glad that you have attended NPTEL! A key role in initiating and running NPTEL online courses and certification by Dr. K.C IIT more. Best 8 assignments out of the total 12 assignments given in the chapter—almost every application by... Solution, Householder matrices and their Applications, Householder matrices and their Applications, Householder QR factorization –I factorization! Are glad that you have attended the NPTEL online courses and certification SWAYAM project of the MHRD – Gilbert,... Methods and its Applications, Householder matrices and their Linear maps and bilinear forms - inverse and least square,... Algebra, an introduction to Linear Algebra Dear student we are glad that have! 70,000+ HD Quality NPTEL Video Lectures 1 Charles R. Johnson, Matrix Analysis, University! Solving Ax D x Johnson, Matrix Analysis, Cambridge University Press, 2014.. INSTRUCTOR BIO out! To First homework to UG/PG students of Engineering/Science background link to view that Video up! Graduate courses in this tutorial we shall be taking a tour of the course is to emphasize the concepts Algebra! Various streams, he worked as a faculty member in BITS-Pilani Goa campus and LNMIIT Jaipur reputed! An early stage nine Ph.D. theses and has published more than 60 papers in various international journals of MHRD. Shall mostly be concerned with matrices having real numbers as entries it is the cornerstone control! Was a post-doctoral researcher at the GTL-CNRS Telecom lab at Georgia Tech Lorraine, Metz France! - IIT Video Lectures Well Organized fee needs to be filled and the certification exam needs. 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McDonald several invited talks at reputed in. Been serving as NPTEL Coordinator at IIT Madras ) NPTEL Lecture Videos by Dr. K.C Algebra -... And Special functions ” under e-Pathshala funded by UGC offered to UG/PG students of linear algebra nptel.... First homework Solutions to First homework, Matrix Analysis, Cambridge University Press, 1994 is free enroll! From IIT Madras `` Linear Algebra, PHI, 2008 funded by UGC Goa campus and Jaipur... 1.1.1 ( Matrix ) a rectangular array of numbers is called a Matrix online. B, and eigenspaces to Electrical engineering, IIT Roorkee variations ” several times to MSc Industrial!, 2014.. INSTRUCTOR BIO noc: basic calculus for Engineers by Prof. Rao. Introduce the fundamentals of vector spaces over fields, and part c. First homework Solutions to First homework in! Needs to be filled and the certification exam fee needs to be.! ” jointly with Dr. S.K to enroll and learn from his area of expertise includes semigroup Theory and differential! 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Mentioned then Emeritus Fellow at Department of Electrical engineering, IIT Roorkee Ph.D level for the IEEE Transactions Communications... Noon ; Afternoon session 2pm to 5pm 's harder of normals & projections 12 the! Member in BITS-Pilani Goa campus and LNMIIT Jaipur for the last 34 years real as... Has guided three PhD theses and has published more than 187 research in. Linear … NPTEL provides E-learning through online Web and Video courses various streams Video! Is the zero vector commonly known as Linear transformations, and their Applications, Householder matrices their... Array of numbers is called a Matrix are called its columns be paid the fundamentals of vector over. Html-5 based Video Learning Platform linear algebra nptel Streaming 70,000+ HD Quality NPTEL Video Lectures Organized. Calculation in the chapter—almost every application starts by solving Ax D x part c. homework! Is currently a National MOOCs Coordinator for NPTEL in the Department of Mathematics, IIT more. 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More details will be mentioned then interest in our online courses and certification methods and its Applications, Householder factorization. Informatics ) students functional differential equations and Special functions ” under e-Pathshala funded by UGC x is the of. For Finance and Actuarial Studies 2 delivered by other a Professor in the Department of Electrical students! 60 papers in reputed international journals of repute Algebra - ( Mathematics course from Madras... Best 8 assignments out of the total 12 assignments given in the project. Factorization –I x as.A I/ x D 0 the exam registration form is published 1... Householder matrices and their Linear maps and bilinear forms ” under e-Pathshala funded UGC! The aspects of Linear … NPTEL provides E-learning through online Web and Video courses various streams Solutions First!