The spectral norm, that is, the square root of λ 1, is the maximum eigenvalue λi of AH * A, where AH is the transposed * * * yoke matrix of a.

Formula: ║A║2? Maximum singular value of = A = (max{ λi(AH*A)})? 1/2 。

Matrix norms derived from other commonly used p- norms;

1- standard:

║A║ 1？ = max{ ∑|ai 1|, ∑|ai2|, ..., ∑|ain|} (column sum norm, the maximum value of the sum of absolute values of elements in each column) (where ∑|ai 1| the sum of absolute values of elements in the first column ∑| ai1| =

Extended data:

Introduction:

Matrix norm is a common basic concept in the fields of matrix theory, linear algebra and functional analysis. When a matrix space is established as a normed vector space, it is the norm of matrix equipment.

In application, the mapping between finite-dimensional normed vector spaces is often expressed in the form of matrix, and the norm of equipment in the mapping space can also be expressed in the form of matrix norm.

Baidu Encyclopedia-Specification

Baidu Encyclopedia-Matrix Specification