norm

norm calculates various matrix norms.

rsNorm = norm(m)

rsNorm = norm(m, ssType)

Return Value

rsNorm is the matrix norm.

Parameters

m

is a real or complex matrix.

ssType

is an option string that sets the matrix norm. It can have one of the following values:

Value	Meaning
“1”	1-Norm (maximum column sum).
“2”	2-Norm (maximum singular value).
“I” oder “Inf”	Infinit Norm (maximum row sum).
“F” oder “Frob”	Frobenius-Norm (Square root of the sum of the aquare of the matrix elements).
“M” oder “Max”	Maximum-Norm (maximum of the absolute value).

Comment

ssType is not case sensitive.

Example

* a = [1,2,3;4,5,6;7,8,9]
* a
   1.0000    2.0000    3.0000
   4.0000    5.0000    6.0000
   7.0000    8.0000    9.0000
* // Calculate various
* // Matrix Norms:
* norm(a)
   18.0000
* norm(a, "1")     // 1-Norm
   18.0000
* max(sum(abs(a)))
   18.0000
* norm(a, "2")    // 2-Norm
   16.8481
* norm(a, "Inf")    // Infinit-Norm
   24.0000
* max(sum(abs(a')))
   24.0000
* norm(a, "Frob")    // Frobenius-Norm
   16.8819
* sqrt(sum(sum(a.*a)))
   16.8819
* norm(a, "m")         // Maximum-Norm
    9.0000
* max(max(abs(a)))
    9.0000

See also

cond

_id-796612