Lecture 1 - Notations, Motivation and Definition Lecture 2 - Matrix: Examples, Transpose and Addition Lecture 3 - Matrix Multiplication Lecture 4 - Matrix Product Recalled Lecture 5 - Matrix Product (Continued...) Lecture 6 - Inverse of a Matrix Lecture 7 - Introduction to System of Linear Equations Lecture 8 - Some Initial Results on Linear Systems Lecture 9 - Row Echelon Form (REF) Lecture 10 - LU Decomposition - Simplest Form Lecture 11 - Elementary Matrices Lecture 12 - Row Reduced Echelon Form (RREF) Lecture 13 - Row Reduced Echelon Form (RREF) (Continued...) Lecture 14 - RREF and Inverse Lecture 15 - Rank of a matrix Lecture 16 - Solution Set of a System of Linear Equations Lecture 17 - System of n Linear Equations in n Unknowns Lecture 18 - Determinant Lecture 19 - Permutations and the Inverse of a Matrix Lecture 20 - Inverse and the Cramer's Rule Lecture 21 - Vector Spaces Lecture 22 - Vector Subspaces and Linear Span Lecture 23 - Linear Combination, Linear Independence and Dependence Lecture 24 - Basic Results on Linear Independence Lecture 25 - Results on Linear Independence (Continued...) Lecture 26 - Basis of a Finite Dimensional Vector Space Lecture 27 - Fundamental Spaces associated with a Matrix Lecture 28 - Rank - Nullity Theorem Lecture 29 - Fundamental Theorem of Linear Algebra Lecture 30 - Definition and Examples of Linear Transformations Lecture 31 - Results on Linear Transformations Lecture 32 - Rank-Nullity Theorem and Applications Lecture 33 - Isomorphism of Vector Spaces Lecture 34 - Ordered Basis of a Finite Dimensional Vector Space Lecture 35 - Ordered Basis (Continued...) Lecture 36 - Matrix of a Linear Transformation Lecture 37 - Matrix of a Linear Transformation (Continued...) Lecture 38 - Matrix of a Linear Transformation (Continued...) Lecture 39 - Similarity of Matrices Lecture 40 - Inner Product Space Lecture 41 - Inner Product (Continued...) Lecture 42 - Cauchy Schwartz Inequality Lecture 43 - Projection on a Vector Lecture 44 - Results on Orthogonality Lecture 45 - Results on Orthogonality (Continued...) Lecture 46 - Gram-Schmidt Orthonormalization Process Lecture 47 - Orthogonal Projections Lecture 48 - Gram-Schmidt Process: Applications Lecture 49 - Examples and Applications on QR-decomposition Lecture 50 - Recapitulate ideas on Inner Product Spaces Lecture 51 - Motivation on Eigenvalues and Eigenvectors Lecture 52 - Examples and Introduction to Eigenvalues and Eigenvectors Lecture 53 - Results on Eigenvalues and Eigenvectors Lecture 54 - Results on Eigenvalues and Eigenvectors (Continued...) Lecture 55 - Results on Eigenvalues and Eigenvectors (Continued...) Lecture 56 - Diagonalizability Lecture 57 - Diagonalizability (Continued...) Lecture 58 - Schur's Unitary Triangularization (SUT) Lecture 59 - Applications of Schur's Unitary Triangularization Lecture 60 - Spectral Theorem for Hermitian Matrices Lecture 61 - Cayley Hamilton Theorem Lecture 62 - Quadratic Forms Lecture 63 - Sylvester's Law of Inertia Lecture 64 - Applications of Quadratic Forms to Analytic Geometry Lecture 65 - Examples of Conics and Quartics Lecture 66 - Singular Value Decomposition (SVD)

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