Learn · Advanced Engineering Mathematics

Lecture 4 of 42Linear Algebra

Linear Transformation, Isomorphism and Matrix Representation

Prof. J. Kumar and others · IIT Kharagpur

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Advanced Engineering Mathematics, IIT Kharagpur (at NPTEL)
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CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures

  1. Review Groups, Fields and Matrices Video
  2. Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors Video
  3. Basis, Dimension, Rank and Matrix Inverse Video
  4. Linear Transformation, Isomorphism and Matrix Representation Video
  5. System of Linear Equations, Eigenvalues and Eigenvectors Video
  6. Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices Video
  7. Jordan Canonical Form, Cayley Hamilton Theorem Video
  8. Inner Product Spaces, Cauchy-Schwarz Inequality Video
  9. Orthogonality, Gram-Schmidt Orthogonalization Process Video
  10. Spectrum of special matrices,positive/negative definite matrices Video
  11. Concept of Domain, Limit, Continuity and Differentiability Video
  12. Analytic Functions, C-R Equations Video
  13. Harmonic Functions Video
  14. Line Integral in the Complex Video
  15. Cauchy Integral Theorem Video
  16. Cauchy Integral Theorem (Contd.) Video
  17. Cauchy Integral Formula Video
  18. Power and Taylor's Series of Complex Numbers Video
  19. Power and Taylor's Series of Complex Numbers (Contd.) Video
  20. Taylor's, Laurent Series of f(z) and Singularities Video
  21. Classification of Singularities, Residue and Residue Theorem Video
  22. Laplace Transform and its Existence Video
  23. Properties of Laplace Transform Video
  24. Evaluation of Laplace and Inverse Laplace Transform Video
  25. Applications of Laplace Transform to Integral Equations and ODEs Video
  26. Applications of Laplace Transform to PDEs Video
  27. Fourier Series Video
  28. Fourier Series (Contd.) Video
  29. Fourier Integral Representation of a Function Video
  30. Introduction to Fourier Transform Video
  31. Applications of Fourier Transform to PDEs Video
  32. Laws of Probability - I Video
  33. Laws of Probability - II Video
  34. Problems in Probability Video
  35. Random Variables Video
  36. Special Discrete Distributions Video
  37. Special Continuous Distributions Video
  38. Joint Distributions and Sampling Distributions Video
  39. Point Estimation Video
  40. Interval Estimation Video
  41. Basic Concepts of Testing of Hypothesis Video
  42. Tests for Normal Populations Video