IsOrthogonal

Tests if a matrix is orthogonal.

Syntax

• IsOrthogonal(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

If A is a matrix, then IsOrthogonal(A, ε) returns true iff A is orthogonal, that is, iff A^−1 = transpose(A). Floating-point numbers are compared with epsilon ε.

Examples

A ≔ RotationMatrix(π/6, ❨1, 2, −1❩)

⎛ 0.888354503154    0.24878234397   0.385919191095⎞
⎜−0.159465946493   0.955341801261   −0.24878234397⎟
⎝−0.430577389833   0.159465946493   0.888354503154⎠

IsOrthogonal(A)

true

See also

• IsUnitary