matrix-l2-norm ( m -- n )
Matrix operations

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Next:	matrix-l-infinity-norm ( m -- n )

Vocabulary
math.matrices

Inputs

m

a matrix

Outputs

n

a number

Word description
Find the norm (size) of a matrix in 𝑙₂ (L^2) vector space, usually written ∥･∥₂.

This is the matrix norm when p=2, and is the square root of the sums of the squares of all the elements of the matrix.

Notes

•	This norm is sometimes called the Hilbert-Schmidt norm.
•	User code should call the generic p-norm instead.
•	This word is the matrix-specific variant of l2-norm.
•	This word is the p = 2 variant of matrix-p-norm.
•	This word is the transpose variant of l1-norm.
•	This word is intended for use with "flat" (2-dimensional) matrices.

Examples

USING: math.matrices prettyprint ; { { 1 1 } { 1 1 } } matrix-l2-norm .
2.0

See also
matrix-l1-norm, matrix-l-infinity-norm, matrix-p-norm, matrix-p-q-norm

Definition

USING: kernel math math.functions sequences ;

IN: math.matrices

: matrix-l2-norm ( m -- n )
    dup zero-matrix?
    [ drop 0 ] [ [ [ sq ] map-sum ] map-sum sqrt ] if ; inline
    foldable flushable