Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

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

The function hadamard computes a bound on the maxnorm of $\det \left(A\right)$ where A is an n by n matrix whose coefficients lie in the domain Z, Q, R, Z[x], Q[x], or R[x].

For Z, the classical inequality of Hadamard is :

 $\prod _{j\]\^2,j=1\mathrm{..}n}\mathrm{sum}(A\[i$ 

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

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

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

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

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

$\sqrt{50}$