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norm

matrix norm

Calling Sequence

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

Arguments

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

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

For vectors

norm(v,p): The l_p norm (sum(v(i)^p))^(1/p) .
norm(v), norm(v,2): The 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 — H-infinity norm
dhnorm — discrete H-infinity norm
h2norm — H2 norm of a continuous time proper dynamical system
abs — absolute value, magnitude
svd — singular value decomposition

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