norm (MATLAB Function Reference)

Vector and matrix norms

n = norm(A)
n = norm(A,p)

Description

The norm of a matrix is a scalar that gives some measure of the magnitude of the elements of the matrix. The norm function calculates several different types of matrix norms:

n = norm(A)

returns the largest singular value of A, max(svd(A)).

n = norm(A,p)

returns a different kind of norm, depending on the value of p:


If p is...	Then `norm` returns...
`1`	The 1-norm, or largest column sum of `A`, `max(sum(abs((A)))`.
`2`	The largest singular value (same as `norm(A)`).
`inf`	The infinity norm, or largest row sum of `A`, `max(sum(abs(A')))`.
`'fro'`	The Frobenius-norm of matrix `A`, `sqrt(sum(diag(A'`*`A)))`.

When A is a vector, slightly different rules apply:


`norm(A,p)`	Returns `sum(abs(A).^`p`)^(1/`p`)`, for any .
`norm(A)`	Returns `norm(A,2)`.
`norm(A,inf)`	Returns `max(abs(A))`.
`norm(A,-inf)`	Returns `min(abs(A))`.

Remarks

To obtain the root-mean-square (RMS) value, use norm(A)/sqrt(n). Note that norm(A), where A is an n-element vector, is the length of A.