Unit 6 · Symmetric Matrices, Positive Definiteness, and the SVD

Chapter 6.1

Symmetric and Positive Definite Matrices

Symmetry buys the best possible spectral news: real eigenvalues and orthonormal eigenvectors. Positive definiteness adds energy — xᵀAx > 0 — and four equivalent tests for it.

13–16 min · in preparation · lesson 16 of 21

By the end

  1. 01State and use the spectral theorem S = QΛQᵀ
  2. 02Test positive definiteness by pivots, eigenvalues, determinants, and energy
  3. 03Connect positive definiteness to minima and ellipsoids

In unit 6

  1. 6.1Symmetric and Positive Definite Matrices13–16
  2. 6.2Matrices in Engineering10–14
  3. 6.3Similar Matrices and the Singular Value Decomposition13–16
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