matrix p-norm

Given a square complex or real matrix A, a matrix norm left double bracketing bar A right double bracketing bar is a nonnegative number associated with A having the properties 1. left double bracketing bar A right double bracketing bar >0 when A!=0 and left double bracketing bar A right double bracketing bar = 0 iff A = 0, 2. left double bracketing bar k A right double bracketing bar = left bracketing bar k right bracketing bar left double bracketing bar A right double bracketing bar for any scalar k, 3. left double bracketing bar A + B right double bracketing bar <= left double bracketing bar A right double bracketing bar + left double bracketing bar B right double bracketing bar , 4. left double bracketing bar A B right double bracketing bar <= left double bracketing bar A right double bracketing bar left double bracketing bar B right double bracketing bar . Let λ_1, ..., λ_n be the eigenvalues of A, then 1/( left double bracketing bar A^(-1) right double bracketing bar )<= left bracketing bar λ right bracketing bar <= left double bracketing bar A right double bracketing bar .

compatible | Frobenius norm | Hilbert-Schmidt norm | maximum absolute column sum norm | maximum absolute row sum norm | natural norm | norm | polynomial norm | spectral norm | spectral radius | vector norm