Frobenius norm

Summary

The Frobenius norm of a matrix is the square root of the sum of the squares of the absolute values of its entries. It is the Euclidean length of the matrix seen as a long vector, and it comes from the inner product $\ip{A}{B} = \tr(B^* A)$. It is a submultiplicative matrix norm that is easy to compute. It equals the square root of the sum of the squares of the singular values.