Unit 7 · Linear Transformations and Applications

Chapter 7.1

Complex Matrices, Fourier, and the FFT

Let vectors go complex: inner products grow conjugates, the Fourier matrix becomes the most useful matrix in engineering, and a factorization trick makes it fast.

12–16 min · in preparation · lesson 19 of 21

By the end

  1. 01Adapt inner products and symmetry to complex vectors and matrices
  2. 02Describe the Fourier matrix and its orthogonality
  3. 03Explain the factorization idea behind the FFT

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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