IsEigenpair

Tests if a scalar and a vector is an eigenpair of a matrix.

Syntax

• IsEigenpair(A, v, λ[, ε])

  • A is a square matrix

  • v is a vector

  • λ is a number

  • ε is a positive number

Description

IsEigenpair(A, v, λ, ε) returns true iff (λ, v) is an eigenpair 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⎠

IsEigenpair(A, ❨1, 0, −1, 1❩, 3)

true

See also

• eigenvalues

• spectrum

• eigenvectors

• IsEigenvector