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Course11110111542 lectures

Basic Linear Algebra

Prof. I.K.Rana · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 1 : Introduction I Video
  2. Lecture 2 : Introduction II Video
  3. Lecture 3 : Introduction III Video
  4. Lecture 4 : Systems of Linear Equations I Video
  5. Lecture 5 : Systems of Linear Equations II Video
  6. Lecture 6 : Systems of Linear Equations III Video

Week 2

  1. Lecture 7 : Reduced Row Echelon Form and Rank I Video
  2. Lecture 8 : Reduced Row Echelon Form and Rank II Video
  3. Lecture 9 : Reduced Row Echelon Form and Rank III Video
  4. Lecture 10 : Solvability of a Linear System, Linear Span, Basis I Video
  5. Lecture 11 : Solvability of a Linear System, Linear Span, Basis II Video
  6. Lecture 12 : Solvability of a Linear System, Linear Span, Basis III Video

Week 3

  1. Lecture 13 : Linear Span, Linear Independence and Basis I Video
  2. Lecture 14 : Linear Span, Linear Independence and Basis II Video
  3. Lecture 15 : Linear Span, Linear Independence and Basis III Video
  4. Lecture 16 : Row Space, Column Space, Rank-Nullity Theorem I Video
  5. Lecture 17 : Row Space, Column Space, Rank-Nullity Theorem II Video
  6. Lecture 18 : Row Space, Column Space, Rank-Nullity Theorem III Video

Week 4

  1. Lecture 19 : Determinants and their Properties I Video
  2. Lecture 20 : Determinants and their Properties II Video
  3. Lecture 21 : Determinants and their Properties III Video

Week 5

  1. Lecture 22 : Linear Transformations I Video
  2. Lecture 23 : Linear Transformations II Video
  3. Lecture 24 : Linear Transformations III Video
  4. Lecture 25 : Orthonormal Basis, Geometry in R^2 I Video
  5. Lecture 26 : Orthonormal Basis, Geometry in R^2 II Video
  6. Lecture 27 : Orthonormal Basis, Geometry in R^2 III Video

Week 6

  1. Lecture 28 : Isometries, Eigenvalues and Eigenvectors I Video
  2. Lecture 29 : Isometries, Eigenvalues and Eigenvectors II Video
  3. Lecture 30 : Isometries, Eigenvalues and Eigenvectors III Video
  4. Lecture 31 : Diagonalization and Real Symmetric Matrices I Video
  5. Lecture 32 : Diagonalization and Real Symmetric Matrices II Video
  6. Lecture 33 : Diagonalization and Real Symmetric Matrices III Video

Week 7

  1. Lecture 34 : Diagonalization and its Applications I Video
  2. Lecture 35 : Diagonalization and its Applications II Video
  3. Lecture 36 : Diagonalization and its Applications III Video

Week 8

  1. Lecture 37 : Abstract Vector Spaces I Video
  2. Lecture 38 : Abstract Vector Spaces II Video
  3. Lecture 39 : Abstract Vector Spaces III Video
  4. Lecture 40 : Inner Product Spaces Video
  5. Lecture 41 : Inner Product Spaces II Video

Live Session

  1. Live Session 08-04-2021 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Mathematics
Teacher
Prof. I.K.Rana
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
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