翻訳と辞書 Words near each other ・ Froan Chapel ・ Frob ・ Frobel ・ Froben Christoph of Zimmern ・ Frobenioid ・ Frobenius ・ Frobenius algebra ・ Frobenius category ・ Frobenius covariant ・ Frobenius determinant theorem ・ Frobenius endomorphism ・ Frobenius Forster ・ Frobenius group ・ Frobenius Institute ・ Frobenius manifold ・ Frobenius matrix ・ Frobenius method ・ Frobenius normal form ・ Frobenius Orgelbyggeri ・ Frobenius pseudoprime ・ Frobenius solution to the hypergeometric equation ・ Frobenius splitting ・ Frobenius theorem ・ Frobenius theorem (differential topology) ・ Frobenius theorem (real division algebras) ・ Frobenius's theorem (group theory) ・ Frobenius–Schur indicator ・ Froberg mutiny ・ Froberville ・ Frobisher 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 Frobenius matrix ： ウィキペディア英語版 Frobenius matrix A Frobenius matrix is a special kind of square matrix from numerical mathematics. A matrix is a Frobenius matrix if it has the following three properties: * all entries on the main diagonal are ones * the entries below the main diagonal of at most one column are arbitrary * every other entry is zero The following matrix is an example. :$A=\backslash begin$ 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & a_ & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & a_ & 0 & \cdots & 1 \end Frobenius matrices are invertible. The inverse of a Frobenius matrix is again a Frobenius matrix, equal to the original matrix with changed signs outside the main diagonal. The inverse of the example above is therefore: :$A^=\backslash begin$ 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & -a_ & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & -a_ & 0 & \cdots & 1 \end Frobenius matrices are named after Ferdinand Georg Frobenius. An alternative name for this class of matrices is Gauss transformation, after Carl Friedrich Gauss.〔Golub and Van Loan, p. 95.〕 They are used in the process of Gaussian elimination to represent the Gaussian transformations. If a matrix is multiplied from the left (left multiplied) with a Frobenius matrix, a linear combination of the remaining rows is added to a particular row of the matrix. Multiplication with the inverse matrix subtracts the corresponding linear combination from the given row. This corresponds to one of the elementary operations of Gaussian elimination (besides the operation of transposing the rows and multiplying a row with a scalar multiple). ==See also== *Elementary matrix, a special case of a Frobenius matrix with only one off-diagonal nonzero 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「Frobenius 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.