Matlab norm 用法小记

 
norm(A,p)

当A是向量时

norm(A,p)  Returnssum(abs(A).^p)^(1/p),forany1<=p<=∞.

norm(A)   Returnsnorm(A,2)

norm(A,inf)  Returnsmax(abs(A)).

norm(A,-inf)  Returnsmin(abs(A)).

当A是矩阵时

n=norm(A)returnsthelargestsingularvalueofA,max(svd(A))

n=norm(A,1)The1-norm,orlargestcolumnsumofA,max(sum(abs(A)).

n=norm(A,2)Thelargestsingularvalue(sameasnorm(A)).

n=norm(A,inf)Theinfinitynorm,orlargestrowsumofA,max(sum(abs(A')))

n=norm(A,'fro')TheFrobenius-normofmatrixA,sqrt(sum(diag(A'*A))).

norm

Vectorandmatrixnorms

Syntax

n[code]

=

norm(A)
n

=

norm(A,p)
[/code]

Description

Thenormofamatrixisascalarthatgivessomemeasureofthemagnitudeoftheelementsofthematrix.The

norm

functioncalculatesseveraldifferenttypesofmatrixnorms:

n=norm(A)

returnsthelargestsingularvalueof

A

,

max(svd(A))

.

n=norm(A,p)

returnsadifferentkindofnorm,dependingonthevalueof

p.

If p is...	Then norm returns...
1	The1-norm,orlargestcolumnsumof A , max(sum(abs(A)) .
2	Thelargestsingularvalue(sameas norm(A) ).
inf	Theinfinitynorm,orlargestrowsumof A , max(sum(abs(A'))) .
'fro'	TheFrobenius-normofmatrix A , sqrt(sum(diag(A' * A))) .

When

A

isavector:

norm(A,p)	Returns sum(abs(A).^p)^(1/p) ,forany1 <= p <= .
norm(A)	Returns norm(A,2) .
norm(A,inf)	Returns max(abs(A)) .
norm(A,-inf)	Returns min(abs(A)) .

Remarks

Notethat

norm(x)

istheEuclideanlengthofavector

x

.Ontheotherhand,MATLABuses"length"todenotethenumberofelements

n

inavector.Thisexampleuses

norm(x)/sqrt(n)

toobtainthe
root-mean-square(RMS)valueofan

n

-elementvector

x

.

x=[0123]
x=
0123

sqrt(0+1+4+9)%Euclideanlength
ans=
3.7417

norm(x)
ans=
3.7417

n=length(x)%Numberofelements
n=
4

rms=3.7417/2%rms=norm(x)/sqrt(n)
rms=
1.8708