Vector and Matrix Norms :: Matrices and Linear Algebra (Mathematics)

Mathematics

Vector and Matrix Norms

The p-norm of a vector x

is computed by norm(x,p). This is defined by any value of p > 1, but the most common values of p are 1, 2, and infinity . The default value is p = 2, which corresponds to Euclidean length.

v = [2 0 -1];
[norm(v,1) norm(v) norm(v,inf)]

ans =
      3.0000    2.2361    2.0000

The p-norm of a matrix A,

The p-norm of matrix A is the max of the p-norm of A times x divided by the p-norm of x

can be computed for p = 1, 2, and infinity by norm(A,p). Again, the default value is p = 2.

C = fix(10*rand(3,2));
[norm(C,1) norm(C) norm(C,inf)]

ans =
     19.0000   14.8015   13.0000

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