NORM

Purpose:

Calculates the norm of a series or array.

NORM(a, mode)

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.

A real representing the norm value.

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

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)))