NORM

Purpose:

Calculates the norm of a series or array.

Syntax:

NORM(a, mode)

a

-

Optional. An input series or array. Defaults to the current Window.

mode

-

Optional. Type of norm calculation. Defaults to 2, the largest singular value. Valid inputs can be any positive integer or:

1:

1-norm. The maximum of the column sum.

2:

Largest singular value (default).

inf:

Maximum of the row sum.

-inf:

Minimum of the row sum.

"fro":

Froenius norm.

Returns:

A real representing the norm value.

Example:

a = {{1, 2, 3},

     {4, 5, 6}, 

     {7, 8, 9}} 

 

norm(a)        returns: 16.848103

norm(a, 1)     returns: 18

norm(a, 2)     returns: 16.848103

norm(a, inf)   returns: 24

norm(a, -inf)  returns: 6

norm(a, "fro") returns: 16.881943

Remarks:

The mode parameter specifies the following norm calculations:

 

Mode    Series Input           ArrayInput

_____________________________________________________

 

   1    sum(mag(m))            max(colsum(mag(m)))  

   2    max(svd(m))            max(svd(m))  

   N    sum(mag(m)^N)/(1/N)    undefined

 inf    max(mag(m))            max(colsum(mag(m)')')

-inf    min(mag(m))            min(colsum(mag(m)')')

"fro"   undefined              sqrt(sum(diag(m' *^ m)))

See Also:

COND

HYPOT

RANK

SVD