Words near each other
 ・ Permsky (inhabited locality) ・ Permsky District ・ Permsky Uyezd ・ Permutable prime ・ Permutation ・ Permutation (album) ・ Permutation (Bill Laswell album) ・ Permutation (disambiguation) ・ Permutation (music) ・ Permutation (policy debate) ・ Permutation automaton ・ Permutation box ・ Permutation City ・ Permutation graph ・ Permutation group ・ Permutation matrix ・ Permutation model ・ Permutation pattern ・ Permutation polynomial ・ Permutation representation (disambiguation) ・ Permutatude theory ・ Permutohedron ・ Permutotetraviridae ・ Permyak Salty Ears ・ Pern ・ PERN Przyjazn SA ・ Pern, Lot ・ Perna ・ Perna (genus) ・ Perna canalicula
 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
 Permutation matrix ： ウィキペディア英語版
Permutation matrix

In mathematics, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix represents a specific permutation of m elements and, when used to multiply another matrix, can produce that permutation in the rows or columns of the other matrix.
== Definition ==

Given a permutation π of ''m'' elements,
:$\pi : \lbrace 1, \ldots, m \rbrace \to \lbrace 1, \ldots, m \rbrace$
given in two-line form by
:$\begin 1 & 2 & \cdots & m \\ \pi\left(1\right) & \pi\left(2\right) & \cdots & \pi\left(m\right) \end,$
its permutation matrix acting on m-dimensional column vectors is the ''m × m'' matrix ''P''π whose entries are all 0 except that in row ''i'', the entry π(''i'') equals 1. We may write
:$P_\pi = \begin \mathbf e_ \\ \mathbf e_ \\ \vdots \\ \mathbf e_ \end,$
where $\mathbf e_j$ denotes a row vector of length ''m'' with 1 in the ''j''th position and 0 in every other position.〔Brualdi (2006) p.2〕

ウィキペディアで「Permutation 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