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Last updated:

September 23, 2023

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FREE

This course includes:

Unlimited Duration

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Description

Matrix Analysis with Applications. Instructors: Dr. S. K. Gupta and Dr. Sanjeev Kumar, Department of Mathematics, IIT Roorkee.

This course contains the concepts related to matrix theory and their applications in various disciplines. It covers a depth understanding of matrix computations involving rank, eigenvalues, eigenvectors, linear transformation, similarity transformations, (diagonalisation, Jordan canonical form, etc). It also involves various iterative methods, including Krylov subspace methods. Finally, topics like positive matrices, non-negative matrices and polar decomposition are discussed in detail with their applications. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Elementary Row Operations Unlimited
  • Lecture 02 – Echelon Form of a Matrix Unlimited
  • Lecture 03 – Rank of a Matrix Unlimited
  • Lecture 04 – System of Linear Equations Unlimited
  • Lecture 05 – System of Linear Equations (cont.) Unlimited
  • Lecture 06 – Introduction to Vector Spaces Unlimited
  • Lecture 07 – Subspaces Unlimited
  • Lecture 08 – Basis and Dimension Unlimited
  • Lecture 09 – Linear Transformations Unlimited
  • Lecture 10 – Rank and Nullity Unlimited
  • Lecture 11 – Inverse of a Linear Transformation Unlimited
  • Lecture 12 – Matrix Associated with a LT Unlimited
  • Lecture 13 – Eigenvalues and Eigenvectors Unlimited
  • Lecture 14 – Cayley-Hamilton Theorem and Minimal Polynomials Unlimited
  • Lecture 15 – Diagonalization Unlimited
  • Lecture 16 – Special Matrices Unlimited
  • Lecture 17 – More on Special Matrices and Gerschgorin Theorem Unlimited
  • Lecture 18 – Inner Product Spaces Unlimited
  • Lecture 19 – Vector and Matrix Norms Unlimited
  • Lecture 20 – Gram Schmidt Process Unlimited
  • Lecture 21 – Normal Matrices Unlimited
  • Lecture 22 – Positive Definite Matrices Unlimited
  • Lecture 23 – Positive Definite and Quadratic Forms Unlimited
  • Lecture 24 – Gram Matrix and Minimization of Quadratic Forms Unlimited
  • Lecture 25 – Generalized Eigenvectors and Jordan Canonical Form Unlimited
  • Lecture 26 – Evaluation of Matrix Functions Unlimited
  • Lecture 27 – Least Square Approximation Unlimited
  • Lecture 28 – Singular Value Decomposition Unlimited
  • Lecture 29 – Pseudo-Inverse and Singular Value Decomposition Unlimited
  • Lecture 30 – Introduction to Ill-conditioned Systems Unlimited
  • Lecture 31 – Regularization of Ill-conditioned Systems Unlimited
  • Lecture 32 – Linear Systems: Iterative Methods I Unlimited
  • Lecture 33 – Linear Systems: Iterative Methods II Unlimited
  • Lecture 34 – Non-stationary Iterative Methods: Steepest Descent I Unlimited
  • Lecture 35 – Non-stationary Iterative Methods: Steepest Descent II Unlimited
  • Lecture 36 – Krylov Subspace Iterative Methods (Conjugate Gradient Method) Unlimited
  • Lecture 37 – Krylov Subspace Iterative Methods (CG and Preconditioning) Unlimited
  • Lecture 38 – Introduction to Positive Matrices Unlimited
  • Lecture 39 – Non-negativity and Irreducible Matrices Unlimited

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