norm

Scilab Function
Last update : 25/04/2007

norm - matrix norms

### Calling Sequence

  `[y]=norm(x [,flag])`

### Parameters

- `x` : real or complex vector or matrix (full or sparse storage)
- `flag` : string (type of norm) (default value =2)

### 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 : `maxi(sum(abs(x),'r'))` ).
  norm(x,'inf'),norm(x,%inf): The infinity norm of `x` (the largest row sum : `maxi(sum(abs(x),'c'))` ).
  norm(x,'fro'): Frobenius norm i.e. `sqrt(sum(diag(x'*x)))`

For vectors

  norm(v,p): l_p norm (`sum(v(i)^p))^(1/p)` .
  norm(v): `=norm(v,2)` : l_2 norm
  norm(v,'inf'): `max(abs(v(i)))` .

### 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` ,