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Course11110413767 lectures

Linear Algebra

Prof. Arbind Kumar Lal · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Notations, Motivation and Definition Video
  2. Matrix: Examples, Transpose and Addition Video
  3. Matrix Multiplication Video
  4. Matrix Product Recalled Video
  5. Matrix Product Continued Video
  6. Inverse of a Matrix Video

Week 2

  1. Introduction to System of Linear Equations Video
  2. Some Initial Results on Linear Systems Video
  3. Row Echelon Form (REF) Video
  4. LU Decomposition - Simplest Form Video
  5. Elementary Matrices Video
  6. Row Reduced Echelon Form (RREF) Video
  7. Row Reduced Echelon Form (RREF) Continued Video
  8. RREF and Inverse Video

Week 3

  1. Rank of a matrix Video
  2. Solution Set of a System of Linear Equations Video
  3. System of n Linear Equations in n Unknowns Video
  4. Determinant Video
  5. Permutations and the Inverse of a Matrix Video
  6. Inverse and the Cramer's Rule Video

Week 4

  1. Vector Spaces Video
  2. Vector Subspaces and Linear Span Video
  3. Linear Combination, Linear Independence and Dependence Video
  4. Basic Results on Linear Independence Video
  5. Results on Linear Independence Continued... Video

Week 5

  1. Basis of a Finite Dimensional Vector Space Video
  2. Fundamental Spaces associated with a Matrix Video
  3. Rank - Nullity Theorem Video
  4. Fundamental Theorem of Linear Algebra Video

Week 6

  1. Definition and Examples of Linear Transformations Video
  2. Results on Linear Transformations Video
  3. Rank-Nullity Theorem and Applications Video
  4. Isomorphism of Vector Spaces Video
  5. Ordered Basis of a Finite Dimensional Vector Space Video

Week 7

  1. Ordered Basis Continued YouTube
  2. Matrix of a Linear transformation YouTube
  3. Matrix of a Linear transformation Continued... YouTube
  4. Matrix of Linear Transformations Continued... YouTube
  5. Similarity of Matrices YouTube

Week 8

  1. Inner Product Space YouTube
  2. Inner Product Continued YouTube
  3. Cauchy Schwartz Inequality YouTube
  4. Projection on a Vector YouTube
  5. Results on Orthogonality YouTube
  6. Results on Orthogonality. YouTube

Week 9

  1. Gram-Schmidt Orthonormalization Process YouTube
  2. Orthogonal Projections YouTube
  3. Gram-Schmidt Process: Applications YouTube
  4. Examples and Applications on QR-decomposition YouTube
  5. Recapitulate ideas on Inner Product Spaces YouTube

Week 10

  1. Motivation on Eigenvalues and Eigenvectors YouTube
  2. Examples and Introduction to Eigenvalues and Eigenvectors YouTube
  3. Results on Eigenvalues and Eigenvectors YouTube
  4. Results on Eigenvalues and Eigenvectors YouTube
  5. Results on Eigenvalues and Eigenvectors. YouTube

Week 11

  1. Diagonalizability YouTube
  2. Diagonalizability Continued... YouTube
  3. Schur's Unitary Triangularization (SUT) YouTube
  4. Applications of Schur's Unitary Triangularization YouTube
  5. Spectral Theorem for Hermitian Matrices YouTube
  6. Cayley Hamilton Theorem YouTube

Week 12

  1. Quadratic Forms YouTube
  2. Sylvester's Law of Inertia YouTube
  3. Applications of Quadratic Forms to Analytic Geometry YouTube
  4. Examples of Conics and Quartics YouTube
  5. Singular Value Decomposition (SVD) YouTube

Live Session

  1. Live Session 20-10-2020 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Arbind Kumar Lal
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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