The natural norm induced by the L^2-norm. Let A^H be the conjugate transpose of the square matrix A, so that (a_(i j))^H = (a^__(j i)), then the spectral norm is defined as the square root of the maximum eigenvalue of A^H A, i.e., left double bracketing bar A right double bracketing bar _2 | = | (maximum eigenvalue of A^H A)^(1/2) | = | max_( left bracketing bar x right bracketing bar _2 !=0) left bracketing bar A x right bracketing bar _2/ left bracketing bar x right bracketing bar _2, This matrix norm is implemented as Norm[m, 2].

L^2-norm | matrix norm | maximum absolute column sum norm | maximum absolute row sum norm

Norm