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Course11110613549 lectures

Linear Algebra

Prof. Pranav Haridas · Kerala School of Mathematics

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Vector Spaces Video
  2. Examples of Vector Spaces Video
  3. Vector Subspaces Video
  4. Linear Combinations and Span Video

Week 2

  1. Linear Independence Video
  2. Basis Video
  3. Dimension Video
  4. Replacement theorem consequences Video

Week 3

  1. Rank Nullity Video
  2. Linear Transformations Video
  3. Linear Transformation Basis Video
  4. Linear Transformation and Matrices Video

Week 4

  1. Problem session Video
  2. Linear Transformation and Matrices continued Video
  3. Invertible Linear Transformations Video
  4. Invertible Linear Transformations and Matrices Video

Week 5

  1. Change of Basis Video
  2. Product of Vector Spaces Video
  3. Quotient Spaces Video
  4. Dual Spaces Video

Week 6

  1. Row operations Video
  2. Rank of a Matrix Video
  3. Inverting matrices Video
  4. Determinants Video

Week 7

  1. Problem Session Video
  2. Diagonal Matrices Video
  3. Eigenvectors and eigenvalues Video
  4. Computing eigenvalues Video

Week 8

  1. Characteristic ploynomia Video
  2. Diagonalizibility Video
  3. Multiplicity of eigenvalues Video
  4. Invariant subspaces Video

Week 9

  1. Complex Vector Spaces Video
  2. Inner Product Spaces Video
  3. Inner Product and Length Video
  4. Orthogonality Video
  5. Problem Session Video

Week 10

  1. Problem Session Video
  2. Orthonormal Basis Video
  3. Gram Schmidt Orthogonalization Video
  4. Orthogonal Complements Video

Week 11

  1. Problem Session Video
  2. Riesz Representation Theorem Video
  3. Adjoint of a linear transformation Video
  4. Properties of the adjoint Video

Week 12

  1. Problem Session Video
  2. Normal Operators Video
  3. Self Adjoint Operators Video
  4. Spectral Theorem Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
Kerala School of Mathematics
Department
Mathematics
Teacher
Prof. Pranav Haridas
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. Coordinated by IIT Madras.
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