Function Repository Resource:

# MatrixNorm

Estimate the Hölder p-norm of a numerical matrix

Contributed by: Jan Mangaldan
 ResourceFunction["MatrixNorm"][m,p] gives an estimate of the Hölder p-norm of the numerical matrix m.

## Details and Options

If the elements of m are exact numbers, ResourceFunction["MatrixNorm"] applies N to them.
For p1 or p, ResourceFunction["MatrixNorm"][m,p] is equivalent to Norm[m,p].
ResourceFunction["MatrixNorm"] takes the following options:
 "Samples" 9 number of samples taken for estimation Tolerance Automatic tolerance for accepting a norm estimate

## Examples

### Basic Examples (2)

Estimate the 2-norm of a rectangular matrix:

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Compare with the result of Norm:

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### Scope (2)

Estimate the 4-norm of a matrix:

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Estimate the 4-norm to arbitrary precision:

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Plot the p-norm of a matrix with varying p:

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### Options (2)

#### Samples (1)

Increase the "Samples" setting to get a better estimate:

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#### Tolerance (1)

Lower the Tolerance setting to get a better estimate:

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### Properties and Relations (3)

MatrixNorm[m,1] is equivalent to Norm[m,1]:

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MatrixNorm[m,∞] is equivalent to Norm[m,∞]:

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For 1<p<∞, MatrixNorm usually gives a good estimate of the p-norm, with less time and effort:

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### Possible Issues (2)

MatrixNorm only works for numerical matrices:

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MatrixNorm only estimates p-norms for p>1:

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## Version History

• 1.0.1 – 04 January 2021
• 1.0.0 – 21 December 2020