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Course10810617151 lectures

Applied Linear Algebra

Prof. Andrew Thangaraj · IIT Madras

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Introduction to the Course Video
  2. Vector Spaces: Introduction Video
  3. Linear Combinations and Span Video
  4. Subspaces, Linear Dependence and Independence Video
  5. Basis and Dimension Video
  6. Sums, Direct Sums and Gaussian Elimination Video

Week 2

  1. Linear Maps and Matrices Video
  2. Null space, Range, Fundamental theorem of linear maps Video
  3. Column space, null space and rank of a matrix Video
  4. Algebraic operations on linear maps Video

Week 3

  1. Invertible maps, Isomorphism, Operators Video
  2. Solving Linear Equations Video
  3. Elementary Row Operations Video
  4. Translates of a subspace, Quotient Spaces Video

Week 4

  1. Row space and rank of a matrix Video
  2. Determinants Video
  3. Coordinates and linear maps under a change of basis Video
  4. Simplifying matrices of linear maps by choice of basis Video

Week 5

  1. Polynomials and Roots Video
  2. Invariant subspaces, Eigenvalues, Eigenvectors Video
  3. More on Eigenvalues, Eigenvectors, Diagonalization Video
  4. Eigenvalues, Eigenvectors and Upper Triangularization Video

Week 6

  1. Properties of Eigenvalues Video
  2. Linear state space equations and system stability Video
  3. Discrete-time Linear Systems and Discrete Fourier Transforms Video
  4. Sequences and counting paths in graphs Video
  5. PageRank Algorithm Video

Week 7

  1. Dot product and length in Cn, Inner product and norm in V over F Video
  2. Orthonormal basis and Gram-Schmidt orthogonalisation Video
  3. Linear Functionals, Orthogonal Complements Video

Week 8

  1. Orthogonal Projection Video
  2. Projection and distance from a subspace Video
  3. Linear equations, Least squares solutions and Linear regression Video
  4. Minimum Mean Squared Error Estimation Video

Week 9

  1. Adjoint of a linear map Video
  2. Properties of Adjoint of a Linear Map Video
  3. Adjoint of an Operator and Operator-Adjoint Product Video

Week 10

  1. Self-adjoint Operator Video
  2. Normal Operators Video
  3. Complex Spectral Theorem Video
  4. Real Spectral Theorem Video

Week 11

  1. Positive Operators Video
  2. Quadratic Forms, Matrix Norms and Optimization Video
  3. Isometries Video
  4. Classification of Operators Video

Week 12

  1. Singular Values and Vectors of a Linear Map Video
  2. Singular Value Decomposition Video
  3. Polar decomposition and some applications of SVD Video

Live Session

  1. Live Session 15-04-2021 Video
  2. Live Session 19-04-2021 Video
  3. Live Session 19-04-2022 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Electrical Engineering
Teacher
Prof. Andrew Thangaraj
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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