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,'inf') is same as NORM(X,inf).

   NORM(X,'fro') is the F-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)).

 

 

  In MATLAB 4.0, if X has complex components, z, then 

  abs(z) = sqrt(z*conj(z)), not abs(real(z)) + abs(imag(z)),

  which was used in some earlier versions of MATLAB.

 

 

  See also COND15XZCU2, RCOND1771ZMC, CONDEST1WJ0ZXH, NORMEST3D7HRZD.