验证一个命题

假设，C为mxn矩阵
则有
trace(C'*C)=norm(C,'fro');


------


>> C = rand(3,3)

C =

0.4898 0.7094 0.6797
0.4456 0.7547 0.6551
0.6463 0.2760 0.1626

>> trace(C'*C)

ans =

2.9227

>> norm(C,'fro')*norm(C,'fro')

ans =

2.9227


--------


help norm
NORM Matrix or vector norm.
For matrices...
NORM(X) is the largest singular value of X, max(svd(X)).
NORM(X,2) is the same as NORM(X).
NORM(X,1) is the 1-norm of X, the largest column sum,
= max(sum(abs(X))).
NORM(X,inf) is the infinity norm of X, the largest row sum,
= max(sum(abs(X'))).
NORM(X,'fro') is the Frobenius norm, sqrt(sum(diag(X'*X))).
NORM(X,P) is available for matrix X only if P is 1, 2, inf or 'fro'.

For vectors...
NORM(V,P) = sum(abs(V).^P)^(1/P).
NORM(V) = norm(V,2).
NORM(V,inf) = max(abs(V)).
NORM(V,-inf) = min(abs(V)).

See also cond, rcond, condest, normest, hypot.

Overloaded methods:
lti/norm
distributed/norm
mfilt.norm
adaptfilt.norm
idmodel/norm
dfilt.norm

Reference page in Help browser
doc norm