IsInvolution

Tests if a matrix is an involution.

Syntax

• IsInvolution(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

IsInvolution(A, ε) returns true iff A is an involution, that is, iff A = A^−1, using ε as the epsilon for floating-point comparisons. Equivalently, A is invertible and A^2 = I (the identity matrix).

Examples

A ≔ ReflectionMatrix(❨3, 1, −2❩)

⎛−0.285714285714  −0.428571428571   0.857142857143⎞
⎜−0.428571428571   0.857142857143   0.285714285714⎟
⎝ 0.857142857143   0.285714285714   0.428571428571⎠

IsInvolution(A)

true

See also

• IsIdempotent