Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[IsOrthogonal], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The function orthog returns true if it can show that the matrix A is orthogonal, false if it can show that the matrix is not orthogonal, and FAIL otherwise.

A matrix is orthogonal if the inner product of any column of A with itself is 1, and the inner product of any column of A with any other column is 0.

The Maple function testeq is used to test whether expressions are equivalent to 0 or 1.

The command with(linalg,orthog) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$A≔\mathrm{array}\left(\left[\left[-\frac{1}{2}\,\frac{\mathrm{sqrt}\left(3\right)}{2}\right]\,\left[\frac{\mathrm{sqrt}\left(3\right)}{2}\,\frac{1}{2}\right]\right]\right)$

$A≔\left[\begin{array}{cc}-\frac{1}{2}& \frac{\sqrt{3}}{2}\\ \frac{\sqrt{3}}{2}& \frac{1}{2}\end{array}\right]$

$\mathrm{orthog}\left(A\right)$

$\mathrm{true}$