A little note on Matlab norm usage

A little note on Matlab norm usage

Matlab norm (a) usage and examples

Norm (A,p)
When a is a vector
Norm (a,p) Returns sum (ABS (A). ^p) ^ (1/p), for any 1 <= p <=∞.
Norm (A) Returns norm (a,2)
Norm (A,inf) Returns Max (ABS (A)).
Norm (A,-inf) Returns min (abs (A)).

When A is a matrix
n = Norm (a) returns the largest singular value of A, Max (SVD (a))
n = Norm (a,1) the 1-norm, or largest column sum of A, Max (SUM (ABS (A)).
n = Norm (a,2) the largest singular value (same as Norm (A)).
n = Norm (a,inf) The Infinity norm, or largest row sum of A, Max (SUM (ABS (A)))
n = Norm (A, ' fro ') the frobenius-norm of Matrix A, sqrt (SUM (diag (a ' *a))).

Norm

Vector and matrix norms

Syntax

• 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 Matrix. The norm function calculates several different types of matrix norms:

n = norm(A) Returns the largest singular value A of max(svd(A)) .

n = norm(A,p) Returns a different kind of norm, depending on the value ofp.

IF&NBSP 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 is A a vector:

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

Remarks

Note that is the norm(x) Euclidean length of a vector x . On the other hand, MATLAB uses "length" to denote the number of elements in n a vector. This example uses to norm(x)/sqrt(n) obtain the Root-mean-square (RMS) is the value of an n -element vector x .

• x = [0 1 2 3]x =      0     1     2     3sqrt (0+1+4+9)   % Euclidean Lengthans =    3.7417norm (x) ans =    3.7417n = Length (x)   % number of ELEMENTSN =     4rms = 3.7417/2  % RMS = norm (x)/sqrt (n) RMS =    1.8708

A little note on Matlab norm usage