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Matric equations

  • C. C. Mac Duffee
Chapter
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Part of the Ergebnisse der Mathematik und Ihrer Grenƶgebiete book series (MATHE1, volume 5)

Abstract

The general linear equation. If A 1 A 2,..., A h , B 1, B 2,..., B h , C are matrices of order n with elements in a field p, the general linear equation is of the form
$$A_1 XB_1 {\text{} } + {\text{} }A_2 XB_2 {\text{} } + {\text{} }...{\text{} } + {\text{} }A_h XB_h {\text{} } = {\text{} }C$$
(46.1)
where X is a matrix of order n, with elements in F, to be found. By replacing C by 0 we obtain the corresponding auxiliary equation. It is evident that if X 1 and X 2 are solutions of (46.1), their difference is a solution of the auxiliary equation. Hence the sum of a particular solution of (46.1) and the general solution of the corresponding auxiliary equation gives the general solution of (46.1).

Keywords

London Math Simple Root Characteristic Root Invariant Factor Great Common Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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