norm norms of a vector or a matrix

## Syntax

            y = norm(x)
            y = norm(x, normType)

## Arguments

x

  vector or matrix of real or complex numbers (full or sparse storage)

normType

  - For a matrix `x`: a number among `1, 2, %inf, -%inf`, or a word among `"inf"` (or `"i"`) or `"fro"` (or `"f"`).
  - For a vector `x`: any number or `%inf`, `-%inf`; or a word `"inf"` (`"i"`), `"fro"` (`"f"`).
  Default value = 2.
y

  norm: single positive real number.

## Description

For matrices

norm(x)

  or `norm(x,2)` is the largest singular value of `x` (`max(svd(x))`).

norm(x,1)

  The l_1 norm `x` (the largest column sum : `max(sum(abs(x),'r'))` ).

norm(x,'inf'),norm(x,%inf)

  The infinity norm of `x` (the largest row sum : `max(sum(abs(x),'c'))` ).

norm(x,'fro')

  Frobenius norm i.e. `sqrt(sum(diag(x'*x)))`.

For vectors

norm(v,p)

  The l_p norm `sum(abs(v(i))^p)^(1/p)` .

norm(v), norm(v,2)

  The l_2 norm

norm(v,'inf')

  `max(abs(v(i)))`.

## Remark

`norm([])` and `norm([],p)` return 0.

`norm(x)` and `norm(x,p)` return NaN if x contains NaNs.

## Examples

    A = [1,2,3];
    norm(A,1)
    norm(A,'inf')
    A = [1,2;3,4]
    max(svd(A)) - norm(A)

    A = sparse([1 0 0 33 -1])
    norm(A)

## See also

- h_norm
- dhnorm
- h2norm
- abs
- svd