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

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Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. A.K. Lal

NPTEL Co-ordinating Institute : IIT Kanpur

NPTEL Lecture Count : 66

NPTEL Course Size : 16 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)


Lecture Titles:

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 - Inner Product Space
Lecture 40 - Inner Product (Continued...)
Lecture 41 - Cauchy Schwartz Inequality
Lecture 42 - Projection on a Vector
Lecture 43 - Results on Orthogonality
Lecture 44 - Results on Orthogonality
Lecture 45 - Gram-Schmidt Orthonormalization Process
Lecture 46 - Orthogonal Projections
Lecture 47 - Gram-Schmidt Process: Applications
Lecture 48 - Examples and Applications on QR-decomposition
Lecture 49 - Recapitulate ideas on Inner Product Spaces
Lecture 50 - Motivation on Eigenvalues and Eigenvectors
Lecture 51 - Examples and Introduction to Eigenvalues and Eigenvectors
Lecture 52 - Results on Eigenvalues and Eigenvectors
Lecture 53 - Results on Eigenvalues and Eigenvectors (Continued...)
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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