请输入您要查询的字词:

 

单词 ProofOfMatrixInverseCalculationByGaussianElimination
释义

proof of matrix inverse calculation by Gaussian elimination


Let A be an invertible matrix, and A-1 its inversePlanetmathPlanetmath, whosecolumns are A1-1,,An-1.Then, by definition of matrix inverse, AA-1=In.But this impliesAA1-1=e1,,AAn-1=en,with e1,,en being the first,,n-th column of Inrespectively.

A being non singular (or invertible), for all kn, AAk-1=ek has a solution for Ak-1, which canbe found by Gaussian eliminationMathworldPlanetmath of [Aek].

The only part that changes between the augmented matricesconstructed is the last column, and these last columns, once theGaussian elimination has been performed, correspond to the columnsof A-1. Because of this, the steps we need to take for theGaussian elimination are the same for each augmented matrix.

Therefore, we can solve the matrix equation by performing Gaussianelimination on [Ae1en], or [AIn].

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 8:31:09