linalg[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
|
|
•
|
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 .
|
•
|
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.
|
|
|
Download Help Document
Was this information helpful?