2
Matrix Theory. Instructor: Prof. Chandra R. Murthy, Department of Electrical Communication Engineering, IISc Bangalore.
FREE
This course includes
Hours of videos
2222 years
Units & Quizzes
80
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
In this course, we will study the basics of matrix theory, with applications to engineering. The focus will be two-fold: on the beautiful mathematical theory of matrices, and their use in solving engineering problems. This course covers topics: Vector spaces, matrices, determinant, rank, etc; Norms, error analysis in linear systems; Eigenvalues and eigenvectors; Canonical, symmetric and Hermitian forms, matrix factorizations; Variational characterizations, the quadratic form; Location and perturbation of eigenvectors; Least-squares problems, generalized inverses; Miscellaneous topics. (from nptel.ac.in)
Course Currilcum
- Lecture 01 – Course Introduction and Properties of Matrices Unlimited
- Lecture 02 – Vector Spaces Unlimited
- Lecture 03 – Basis, Dimension Unlimited
- Lecture 04 – Linear Transforms Unlimited
- Lecture 05 – Fundamental Subspaces of a Matrix Unlimited
- Lecture 06 – Fundamental Theorem of Linear Algebra Unlimited
- Lecture 07 – Properties of Rank Unlimited
- Lecture 08 – Inner Product Unlimited
- Lecture 09 – Gram-Schmidt Algorithm Unlimited
- Lecture 10 – Orthonormal Matrices Definition Unlimited
- Lecture 11 – Determinant Unlimited
- Lecture 12 – Properties of Determinants Unlimited
- Lecture 13 – Introduction to Norms and Inner Products Unlimited
- Lecture 14 – Vector Norms and their Properties Unlimited
- Lecture 15 – Applications and Equivalence of Vector Norms Unlimited
- Lecture 16 – Summary of Equivalence of Norms Unlimited
- Lecture 17 – Dual Norms Unlimited
- Lecture 18 – Properties and Examples of Dual Norms Unlimited
- Lecture 19 – Matrix Norms Unlimited
- Lecture 20 – Matrix Norms: Properties Unlimited
- Lecture 21 – Induced Norms Unlimited
- Lecture 22 – Induced Norms and Examples Unlimited
- Lecture 23 – Spectral Radius Unlimited
- Lecture 24 – Properties of Spectral Radius Unlimited
- Lecture 25 – Convergent Matrices, Banach Lemma Unlimited
- Lecture 26 – Recap of Matrix Norms and Levy-Desplanques Theorem Unlimited
- Lecture 27 – Equivalence of Matrix Norms and Error in Inverse of Linear Systems Unlimited
- Lecture 28 – Errors in Inverses of Matrices Unlimited
- Lecture 29 – Errors in Solving Systems of Linear Equations Unlimited
- Lecture 30 – Introduction to Eigenvalues and Eigenvectors Unlimited
- Lecture 31 – The Characteristic Polynomial Unlimited
- Lecture 32 – Solving Characteristic Polynomials, Eigenvector Properties Unlimited
- Lecture 33 – Similarity Unlimited
- Lecture 34 – Diagonalization Unlimited
- Lecture 35 – Relationship between Eigenvalues of BA and AB Unlimited
- Lecture 36 – Eigenvector and Principle of Biorthogonality Unlimited
- Lecture 37 – Unitary Matrices Unlimited
- Lecture 38 – Properties of Unitary Matrices Unlimited
- Lecture 39 – Unitary Equivalence Unlimited
- Lecture 40 – Schur’s Triangularization Theorem Unlimited
- Lecture 41 – Cayley-Hamilton Theorem Unlimited
- Lecture 42 – Uses of Cayley-Hamilton Theorem and Diagonalizability Revisited Unlimited
- Lecture 43 – Normal Matrices: Definition and Fundamental Properties Unlimited
- Lecture 44 – Fundamental Properties of Normal Matrices Unlimited
- Lecture 45 – QR Decomposition and Canonical Forms Unlimited
- Lecture 46 – Jordan Canonical Form Unlimited
- Lecture 47 – Determining the Jordan Form of a Matrix Unlimited
- Lecture 48 – Properties of the Jordan Canonical Form, Part 1 Unlimited
- Lecture 49 – Properties of the Jordan Canonical Form, Part 2 Unlimited
- Lecture 50 – Properties of Convergent Matrices Unlimited
- Lecture 51 – Polynomials and Matrices Unlimited
- Lecture 52 – Gaussian Elimination and LU Factorization Unlimited
- Lecture 53 – LU Decomposition Unlimited
- Lecture 54 – LU Decomposition with Pivoting Unlimited
- Lecture 55 – Solving Pivoted System and LDM Decomposition Unlimited
- Lecture 56 – Cholesky Decomposition and Uses Unlimited
- Lecture 57 – Hermitian and Symmetric Matrix Unlimited
- Lecture 58 – Properties of Hermitian Matrices Unlimited
- Lecture 59 – Variational Characterization of Eigenvalues: Rayleigh-Ritz Theorem Unlimited
- Lecture 60 – Variational Characterization of Eigenvalues (cont.) Unlimited
- Lecture 61 – Courant-Fischer Theorem Unlimited
- Lecture 62 – Summary of Rayleigh-Ritz and Courant-Fischer Theorems Unlimited
- Lecture 63 – Weyl’s Theorem Unlimited
- Lecture 64 – Positive Semi-definite Matrix, Monotonicity Theorem and Interlacing Theorems Unlimited
- Lecture 65 – Interlacing Theorem I Unlimited
- Lecture 66 – Interlacing Theorem II (Converse) Unlimited
- Lecture 67 – Interlacing Theorem (cont.) Unlimited
- Lecture 68 – Eigenvalues: Majorization Theorem and Proof Unlimited
- Lecture 69 – Location and Perturbation of Eigenvalues: Dominant Diagonal Theorem Unlimited
- Lecture 70 – Location and Perturbation of Eigenvalues: Gershgorin’s Theorem Unlimited
- Lecture 71 – Implications of Gershgorin Disc Theorem, Condition of Eigenvalues Unlimited
- Lecture 72 – Condition of Eigenvalues for Diagonalizable Matrices Unlimited
- Lecture 73 – Perturbation of Eigenvalues: Birkhoff’s Theorem, Hoffman-Wielandt Theorem Unlimited
- Lecture 74 – Singular Value Definition and Some Remarks Unlimited
- Lecture 75 – Proof of Singular Value Decomposition Theorem Unlimited
- Lecture 76 – Partitioning the SVD Unlimited
- Lecture 77 – Properties of SVD Unlimited
- Lecture 78 – Generalized Inverse of Matrices Unlimited
- Lecture 79 – Least Squares Unlimited
- Lecture 80 – Constrained Least Squares Unlimited
