NOC:Linear Algebra (Prof. A.K. Lal)

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)