n = norm(X)
n = norm(X,p)
n = norm(X,'fro')
n = norm(X)
, where X
is a matrix, is the largest singular value of X
.
n = norm(X,p)
, lets you specify a value to indicate largest singular value, largest column sum, or largest row sum of matrix X
:
norm(X,1)
is the 1-norm, or largest column sum of X
, max(sum(abs((X)))
.norm(X,2)
is the same as norm(X)
.norm(X,inf)
is the infinity norm, or largest row sum of X
, max(sum(abs(X')))
.n = norm(X,'fro')
is the F-norm of matrix X
, sqrt(sum(diag(X'
*X)))
.
When the X
is a vector, slightly different rules apply:
norm(x,p) = sum(abs(x).^p)^(1/p)
.norm(x) = norm(x,2)
.norm(x)/sqrt(n)
is the root-mean-square (RMS) value.norm(x,inf) = max(abs(x))
.norm(x, -inf) = min(abs(x))
.
For a vectorA =
1 2 3
4 5 6
7 8 9
norm(A) = 16.8481
norm(A,1) = 18
norm(A,2) = 16.8481
norm(A,inf) = 24
norm(A,'fro') = 16.8819
v =
1 2 3
norm(v) = 3.7417
norm(v,1) = 6
norm(v,2) = 3.7417
norm(v,Inf) = 3
norm(v,pi) = 3.2704
cond
,max
,min
,rcond
,svd
(c) Copyright 1994 by The MathWorks, Inc.