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linalg(deprecated)

  

norm

  

norm of a matrix or vector

 

Calling Sequence

Parameters

Description

Examples

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 AhtransposeA .

• 

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.

withlinalg:

normarray1,2,3,4,∞

7

(1)

normarray1,1,2,2

6

(2)

normarray1,1,2,1.367

3.043660199

(3)

See Also

linalg(deprecated)[cond]

LinearAlgebra

LinearAlgebra[ConditionNumber]

LinearAlgebra[Norm]

VectorCalculus[Norm]