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If there is a repeated eigenvalue, there may not be ''n'' independent eigenvalues. If there is a repeated eigenvalue, there may not be ''n'' independent eigenvectors.

Eigenvalues and Eigenvectors

Contents

  1. Eigenvalues and Eigenvectors
    1. Definition
      1. Properties

Definition

Eigenvalues and eigenvectors are paired. For an invertible n x n matrix, there should be n pairs. They satisfy the conditions Ax = λx and |A - λI| = 0.

If there is a repeated eigenvalue, there may not be n independent eigenvectors.

Properties

Adding nI to A does not change its eigenvectors and adds n to the eigenvalues.

The sum of the eigenvalues is the trace (sum of diagonal). The product of the eigenvalues is the determinant.

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LinearAlgebra/EigenvaluesAndEigenvectors (last edited 2024-02-06 05:04:28 by DominicRicottone)