Ky fan norm

A Ky-Fan standard is a special standard named after Ky Fan for the space of the matrices . There are a number of Ky-Fan norms that are indexed by a natural number . ${\ displaystyle k}$

definition

The -th Ky-Fan norm of a matrix is defined as ${\ displaystyle k}$ ${\ displaystyle A}$

{\ displaystyle \ | A \ | _ {k}: = s_ {1} (A) + s_ {2} (A) + \ cdots + s_ {k} (A),}

where is the -th singular value of . ${\ displaystyle s_ {i} (A)}$ ${\ displaystyle i}$ ${\ displaystyle A}$

Individual evidence

^ Rajendra Bhatia: Matrix analysis . Springer, New York 1997, ISBN 0-387-94846-5 , pp. 92 .

[Bhatia92-1] Rajendra Bhatia: Matrix analysis . Springer, New York 1997, ISBN 0-387-94846-5 , pp. 92 .