EigenvectorOf

Finds an eigenvector for a given eigenvalue.

Syntax

• EigenvectorOf(A, λ)

  • A is a matrix

  • λ is an eigenvalue of A

Description

If λ is an eigenvalue of A, then EigenvectorOf(A, λ) returns an eigenvector of A corresponding to λ.

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⎠

EigenvectorOf(A, 3)

 ⎛0.57735026919 ⎞
 ⎜      0       ⎟
e⎜−0.57735026919⎟
 ⎝0.57735026919 ⎠

See also

• eigenvalues

• spectrum

• eigenvectors

• EigenvalueOf