Advanced Matrix Theory and Linear Algebra

Indian Institute of Science Bangalore

Course Outline: Introduction, Vector Spaces, Solutions of Linear Systems, Important Subspaces associated with a matrix, Orthogonality, Eigenvalues and Eigenvectors, Diagonalizable Matrices, Hermitian Matrices, General Matrices, Jordan Canonical form (optional), Selected Topics in Applications (optional).

• Mod-01 Lec-01 Prologue Part 1
Prof. Vittal Rao
• Mod-01 Lec-02 Prologue Part 2
Prof. Vittal Rao
• Mod-01 Lec-03 Prologue Part 3
Prof. Vittal Rao
• Mod-02 Lec-04 Linear Systems Part 1
Prof. Vittal Rao
• Mod-02 Lec-05 Linear Systems Part 2
Prof. Vittal Rao
• Mod-02 Lec-06 Linear Systems Part 3
Prof. Vittal Rao
• Mod-02 Lec-07 Linear Systems Part 4
Prof. Vittal Rao
• Mod-03 Lec-08 Vector Spaces Part 1
Prof. Vittal Rao
• Mod-03 Lec-09 Vector Spaces Part 2
Prof. Vittal Rao
• Mod-04 Lec-10 Linear Independence and Subspaces Part 1
Prof. Vittal Rao
• Mod-04 Lec-11 Linear Independence and Subspaces Part 2
Prof. Vittal Rao
• Mod-04 Lec-12 Linear Independence and Subspaces Part 3
Prof. Vittal Rao
• Mod-04 Lec-13 Linear Independence and Subspaces Part 4
Prof. Vittal Rao
• Mod-05 Lec-14 Basis Part 1
Prof. Vittal Rao
• Mod-05 Lec-15 Basis Part 2
Prof. Vittal Rao
• Mod-05 Lec-16 Basis Part 3
Prof. Vittal Rao
• Mod-06 Lec-17 Linear Transformations Part 1
Prof. Vittal Rao
• Mod-06 Lec-18 Linear Transformations Part 2
Prof. Vittal Rao
• Mod-06 Lec-19 Linear Transformations Part 3
Prof. Vittal Rao
• Mod-06 Lec-20 Linear Transformations Part 4
Prof. Vittal Rao
• Mod-06 Lec-21 Linear Transformations Part 5
Prof. Vittal Rao
• Mod-07 Lec-22 Inner Product and Orthogonality Part 1
Prof. Vittal Rao
• Mod-07 Lec-23 Inner Product and Orthogonality Part 2
Prof. Vittal Rao
• Mod-07 Lec-24 Inner Product and Orthogonality Part 3
Prof. Vittal Rao
• Mod-07 Lec-25 Inner Product and Orthogonality Part 4
Prof. Vittal Rao
• Mod-07 Lec-26 Inner Product and Orthogonality Part 5
Prof. Vittal Rao
• Mod-07 Lec-27 Inner Product and Orthogonality Part 6
Prof. Vittal Rao
• Mod-08 Lec-28 Diagonalization Part 1
Prof. Vittal Rao
• Mod-08 Lec-29 Diagonalization Part 2
Prof. Vittal Rao
• Mod-08 Lec-30 Diagonalization Part 3
Prof. Vittal Rao
• Mod-08 Lec-31 Diagonalization Part 4
Prof. Vittal Rao
• Mod-09 Lec-32 Hermitian and Symmetric matrices Part 1
Prof. Vittal Rao
• Mod-09 Lec-33 Hermitian and Symmetric matrices Part 2
Prof. Vittal Rao
• Mod-09 Lec-34 Hermitian and Symmetric matrices Part 3
Prof. Vittal Rao
• Mod-09 Lec-35 Hermitian and Symmetric matrices Part 4
Prof. Vittal Rao
• Mod-10 Lec-36 Singular Value Decomposition (SVD) Part 1
Prof. Vittal Rao
• Mod-10 Lec-37 Singular Value Decomposition (SVD) Part 2
Prof. Vittal Rao
• Mod-11 Lec-38 Back To Linear Systems Part 1
Prof. Vittal Rao
• Mod-11 Lec-39 Back To Linear Systems Part 2
Prof. Vittal Rao
• Mod-12 Lec-40 Epilogue
Prof. Vittal Rao