Unit 7 · Linear Transformations and Applications

Chapter 7.2

Linear Transformations and Choice of Basis

Behind every matrix is a linear map; behind every basis, a different matrix for the same map. Choosing the basis well is what diagonalization and the SVD were secretly doing.

12–16 min · in preparation · lesson 20 of 21

By the end

  1. 01Verify linearity and build the matrix of a transformation in a given basis
  2. 02Change basis and explain similarity as re-description
  3. 03Pick bases that make a transformation's matrix simple

In unit 7

  1. 7.1Complex Matrices, Fourier, and the FFT12–16
  2. 7.2Linear Transformations and Choice of Basis12–16
  3. 7.3Linear Programming and Computation12–16
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