IsEigenvector

Tests if a vector is an eigenvector of a matrix.

Syntax

• IsEigenvector(A, v, [, ε])

  • A is a square matrix

  • v is a vector

  • ε is a positive number

Description

IsEigenvector(A, v, ε) returns true iff v is an eigenvector of A with floating-point comparisons made with epsilon ε.

Examples

A ≔ ❨❨1, −1, −1, 1❩, ❨−1, 0, 0, 1❩, ❨−1, 0, 2, 0❩, ❨1, 0, 0, 2❩❩

⎛ 1  −1  −1   1⎞
⎜−1   0   0   1⎟
⎜−1   0   2   0⎟
⎝ 1   0   0   2⎠

IsEigenvector(A, ❨1, 0, −1, 1❩)

true

See also

• eigenvalues

• spectrum

• eigenvectors

• IsEigenpair