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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Cyclic subspace ： ウィキペディア英語版 Cyclic subspace In mathematics, in linear algebra, a cyclic subspace is a certain special subspace of a finite-dimensional vector space associated with a vector in the vector space and a linear transformation of the vector space. The cyclic subspace associated with a vector ''v'' in a vector space ''V'' and a linear transformation ''T'' of ''V'' is called the ''T''-cyclic subspace generated by ''v''. The concept of a cyclic subspace is a basic component in the formulation of the cyclic decomposition theorem in linear algebra. ==Definition== Let $T:V\backslash rightarrow\; V$ be a linear transformation of a vector space $V$ and let $v$ be a vector in $V$. The $T$-cyclic subspace of $V$ generated by $v$ is the subspace $W$ of $V$ generated by the set of vectors $\backslash$. This subspace is denoted by $Z(v;T)$. If $V=Z(v;T)$, then $v$ is called a cyclic vector for $T$. There is another equivalent definition of cyclic spaces. Let $T:V\backslash rightarrow\; V$ be a linear transformation of a finite dimensional vector space over a field $F$ and $v$ be a vector in $V$. The set of all vectors of the form $g(T)v$, where $g(x)$ is a polynomial in the ring $F()$ of all polynomials in $x$ over $F$, is the $T$-cyclic subspace generated by $v$.〔 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「Cyclic subspace」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.