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Advanced Matrix Theory and Linear Algebra for Engineers. Instructor: Prof. Vittal Rao, Centre for Electronics Design and Technology, IISc Bangalore.
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Description
Introduction to systems of linear equations, Vector spaces, Solutions of linear systems, Important subspaces associated with a matrix, Orthogonality, Eigenvalues and eigenvectors, Diagonalizable matrices, Hermitian and symmetric matrices, General matrices. (from nptel.ac.in)
Course content
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- Lecture 01 – Prologue Part 1: Systems of Linear Equations, Matrix Notation Unlimited
- Lecture 02 – Prologue Part 2: Diagonalization of a Square Matrix Unlimited
- Lecture 03 – Prologue Part 3: Homogeneous Systems, Elementary Row Operations Unlimited
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- Lecture 04 – Linear Systems 1: Elementary Row Operations (EROs) Unlimited
- Lecture 05 – Linear Systems 2: Row Reduced Echelon Form, The Reduction Process Unlimited
- Lecture 06 – Linear Systems 3: The Reduction Process, Solution using EROs Unlimited
- Lecture 07 – Linear Systems 4: Solution using EROs: Non-homogeneous Systems Unlimited
- Lecture 08 – Vector Spaces Part 1 Unlimited
- Lecture 09 – Vector Spaces Part 2 Unlimited
- Lecture 14 – Basis, Basis as a Maximal Linearly Independent Set Unlimited
- Lecture 15 – Finite Dimensional Vector Spaces Unlimited
- Lecture 16 – Extension of a Linearly Independent Set to a Basis, Ordered Basis Unlimited
- Lecture 22 – Inner Product and Orthogonality Unlimited
- Lecture 23 – Orthonormal Sets, Orthonormal Basis and Fourier Expansion Unlimited
- Lecture 24 – Fourier Expansion, Gram-Schmidt Orthonormalization, Orthogonal Complements Unlimited
- Lecture 25 – Orthogonal Complements, Decomposition of a Vector, Pythagoras Theorem Unlimited
- Lecture 26 – Orthogonal Complements in the context of Subspaces Associated with a Matrix Unlimited
- Lecture 27 – Best Approximation Unlimited
- Lecture 32 – Hermitian and Symmetric Matrices, Unitary Matrix Unlimited
- Lecture 33 – Unitary and Orthogonal Matrices, Eigen Properties of Hermitian Matrices, … Unlimited
- Lecture 34 – Spectral Decomposition Unlimited
- Lecture 35 – Positive and Negative Definite and Semidefinite Matrices Unlimited
- Lecture 38 – Back to Linear Systems Part 1 Unlimited
- Lecture 39 – Back to Linear Systems Part 2 Unlimited
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