请输入您要查询的字词:

 

单词 InverseOfMatrixWithSmallrankAdjustment
释义

inverse of matrix with small-rank adjustment


Suppose that an n×n matrix B is obtained by adding asmall-rank adjustment XRYT to matrix A,

B=A+XRYT,

where X and Y are n×r matrices, and R is an r×r matrix. Assume that the inverse of A is known and r is muchsmaller than n. The following formula for B-1 is oftenuseful,

B-1=A-1-A-1X(R-1+YTA-1X)-1YTA-1

provided that all inverses in the formula exist.

In particular, when r=1 and A=I, we have

(I+xyT)-1=I-xyT1+yTx

for any n×1 column vectorsMathworldPlanetmath x and y such that 1+yTx0.

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 16:07:52