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

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

The function cond computes the ``standard'' matrix condition number, defined as norm(A) * norm(inverse(A)). The matrix norm is the default employed by the linalg[norm] function, namely the infinity norm (maximum row sum).

More generally, cond(A, normname) computes norm(A, normname) * norm(inverse(A), normname). This is the same measure, but using the specified norm instead of the infinity norm.

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

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

$B≔\mathrm{array}\left(1..2\,1..2\,\mathrm{identity}\right)$

$B≔\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$\mathrm{cond}\left(B\right)$

$1$

$A≔\mathrm{matrix}\left(3\,3\,\left[1\,0\,3\,-4\,2\,0\,0\,3\,-2\right]\right)$

$A≔\left[\begin{array}{ccc}1& 0& 3\\ \mathrm{-4}& 2& 0\\ 0& 3& \mathrm{-2}\end{array}\right]$

$\mathrm{cond}\left(A\,1\right)$

$3$