linalg(deprecated)

 bound on coefficients of a determinant

Parameters

 A - square matrix

Description

 • 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 $\mathrm{det}\left(A\right)$ 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 :
 $\prod _{j]^2,j=1\mathrm{..}n}\mathrm{sum}\left(A[i$
 • The command with(linalg,hadamard) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{matrix}\left(3,3,\left[1,-1,0,0,2,-1,-2,0,1\right]\right)$
 ${A}{≔}\left[\begin{array}{ccc}{1}& {-1}& {0}\\ {0}& {2}& {-1}\\ {-2}& {0}& {1}\end{array}\right]$ (1)
 > $\mathrm{hadamard}\left(A\right)$
 $\sqrt{{50}}$ (2)