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.

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

$\mathrm{norm}\left(\mathrm{array}\left(\left[\left[1\,-2\right]\,\left[3\,-4\right]\right]\right)\,\mathrm{\infty }\right)$

$7$

$\mathrm{norm}\left(\mathrm{array}\left(\left[1\,-1\,2\right]\right)\,2\right)$

$\sqrt{6}$

$\mathrm{norm}\left(\mathrm{array}\left(\left[1\,-1\,2\right]\right)\,1.367\right)$

$3.043660199$