翻訳と辞書 Words near each other ・ Model ・ Model (art) ・ Model (band) ・ Model (people) ・ Model (surname) ・ Model (TV series) ・ Model 1 ・ Model 10 ・ Model 102 telephone ・ Modal dispersion ・ Modal fictionalism ・ Modal frame ・ Modal haplotype ・ Modal jazz ・ Modal logic ・ Modal matrix ・ Modal operator ・ Modal particle ・ Modal property ・ Modal realism ・ Modal scope fallacy ・ Modal share ・ Modal Soul ・ Modal Soul Classics ・ Modal Soul Classics II ・ Modal testing ・ Modal verb ・ Modal voice ・ Modal window ・ Modal μ-calculus Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Modal matrix ： ウィキペディア英語版 Modal matrix In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors. Specifically the modal matrix $M$ for the matrix $A$ is the ''n'' × ''n'' matrix formed with the eigenvectors of $A$ as columns in $M$. It is utilized in the similarity transformation : $D\; =\; M^AM,$ where $D$ is an ''n'' × ''n'' diagonal matrix with the eigenvalues of $A$ on the main diagonal of $D$ and zeros elsewhere. The matrix $D$ is called the spectral matrix for $A$. The eigenvalues must appear left to right, top to bottom in the same order as their corresponding eigenvectors are arranged left to right in $M$. == Example == The matrix :$A\; =\; \backslash begin$ 3 & 2 & 0 \\ 2 & 0 & 0 \\ 1 & 0 & 2 \end has eigenvalues and corresponding eigenvectors :$\backslash lambda\_1\; =\; -1,\; \backslash quad\; \backslash ,\; \backslash bold\; b\_1\; =\; \backslash left(\; -3,\; 6,\; 1\; \backslash right)\; ,$ :$\backslash lambda\_2\; =\; 2,\; \backslash qquad\; \backslash bold\; b\_2\; =\; \backslash left(\; 0,\; 0,\; 1\; \backslash right)\; ,$ :$\backslash lambda\_3\; =\; 4,\; \backslash qquad\; \backslash bold\; b\_3\; =\; \backslash left(\; 2,\; 1,\; 1\; \backslash right)\; .$ A diagonal matrix $D$, similar to $A$ is :$D\; =\; \backslash begin$ -1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end. One possible choice for an invertible matrix $M$ such that $D\; =\; M^AM,$ is :$M\; =\; \backslash begin$ -3 & 0 & 2 \\ 6 & 0 & 1 \\ 1 & 1 & 1 \end. Note that since eigenvectors themselves are not unique, and since the columns of both $M$ and $D$ may be interchanged, it follows that both $M$ and $D$ are not unique. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Modal matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.