linalg(deprecated)/norm - Maple Help

linalg(deprecated)

 norm
 norm of a matrix or vector

 Calling Sequence norm(A) norm(A, normname)

Parameters

 A - matrix or vector normname - (optional) matrix/vector norm

Description

 • Important: The linalg package has been deprecated. Use the superseding command, LinearAlgebra[Norm], instead.
 - For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
 • The function norm(A, normname) computes the specified matrix or vector norm for the matrix or vector A.
 • For matrices, normname should be one of: 1, 2, 'infinity', 'frobenius'.
 • For vectors, normname should be one of: any real constants >=1, 'infinity', 'frobenius'.
 • The default norm used throughout the linalg package is the infinity norm.  Thus norm(A) computes the infinity norm of A and is equivalent to norm(A, infinity).
 • For vectors, the infinity norm is the maximum magnitude of all elements. The infinity norm of a matrix is the maximum row sum, where the row sum is the sum of the magnitudes of the elements in a given row.
 • The frobenius norm of a matrix or vector is defined to be the square root of the sum of the squares of the magnitudes of each element.
 • The '1'-norm of a matrix is the maximum column sum, where the column sum is the sum of the magnitudes of the elements in a given column. The '2'-norm of a matrix is the square root of the maximum eigenvalue of the matrix $A\mathrm{htranspose}\left(A\right)$ .
 • For a positive integer k, the k-norm of a vector is the kth root of the sum of the magnitudes of each element raised to the kth power.
 • The command with(linalg,norm) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $\mathrm{norm}\left(\mathrm{array}\left(\left[\left[1,-2\right],\left[3,-4\right]\right]\right),\mathrm{\infty }\right)$
 ${7}$ (1)
 > $\mathrm{norm}\left(\mathrm{array}\left(\left[1,-1,2\right]\right),2\right)$
 $\sqrt{{6}}$ (2)
 > $\mathrm{norm}\left(\mathrm{array}\left(\left[1,-1,2\right]\right),1.367\right)$
 ${3.043660199}$ (3)