**'org.ejml.ops.NormOps'**Java class

org.ejml.ops

## Class NormOps

- java.lang.Object
- org.ejml.ops.NormOps

public class NormOpsextends Object

Norms are a measure of the size of a vector or a matrix. One typical application is in error analysis.

Vector norms have the following properties:

- ||x|| > 0 if x ≠ 0 and ||0|| = 0
- ||αx|| = |α| ||x||
- ||x+y|| ≤ ||x|| + ||y||

Matrix norms have the following properties:

- ||A|| > 0 if A ≠ 0 where A ∈ ℜ
^{m × n} - || α A || = |α| ||A|| where A ∈ ℜ
^{m × n} - ||A+B|| ≤ ||A|| + ||B|| where A and B are ∈ ℜ
^{m × n} - ||AB|| ≤ ||A|| ||B|| where A and B are ∈ ℜ
^{m × m}

Matrix norms can be induced from vector norms as is shown below:

||A||_{M}= max_{x≠0}||Ax||_{v}/||x||_{v}

where ||.||_{M}is the induced matrix norm for the vector norm ||.||_{v}.By default implementations that try to mitigate overflow/underflow are used. If the word fast is found before a function's name that means it does not mitigate those issues, but runs a bit faster.

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