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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 Bott–Duffin inverse ： ウィキペディア英語版 Constrained generalized inverse In linear algebra, a constrained generalized inverse is obtained by solving a system of linear equations with an additional constraint that the solution is in a given subspace. One also says that the problem is described by a system of constrained linear equations. In many practical problems, the solution $x$ of a linear system of equations :$$ Ax=b\qquad (\textA\in\R^\text b\in\R^m) is acceptable only when it is in a certain linear subspace $L$ of $\backslash R^m$. In the following, the orthogonal projection on $L$ will be denoted by $P\_L$. Constrained system of linear equations :$Ax=b\backslash qquad\; x\backslash in\; L$ has a solution if and only if the unconstrained system of equations :$(A\; P\_L)\; x\; =\; b\backslash qquad\; x\backslash in\backslash R^m$ is solvable. If the subspace $L$ is a proper subspace of $\backslash R^m$, then the matrix of the unconstrained problem $(A\; P\_L)$ may be singular even if the system matrix $A$ of the constrained problem is invertible (in that case, $m=n$). This means that one needs to use a generalized inverse for the solution of the constrained problem. So, a generalized inverse of $(A\; P\_L)$ is also called a $L$-''constrained pseudoinverse'' of $A$. An example of a pseudoinverse that can be used for the solution of a constrained problem is the Bott-Duffin inverse of $A$ constrained to $L$, which is defined by the equation :$A\_L^:=P\_L(A\; P\_L\; +\; P\_)^,$ if the inverse on the right-hand-side exists. 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「Constrained generalized inverse」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.