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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 Matrix representation of conic sections ： ウィキペディア英語版 Matrix representation of conic sections In mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. We can also study conic sections whose axes are not parallel to our coordinate system. Conic sections have the form of a second-degree polynomial: :$$ Q \ \stackrel\ Ax^2+Bxy+Cy^2+Dx+Ey+F=0. \, This can be written as: :$$ \mathbf^T A_Q\mathbf=0, where $\backslash mathbf$ is the homogeneous coordinate vector :$$ \begin x \\ y \\ 1 \end and where $A\_Q$ is a matrix: :$$ A_Q = \begin A & B/2 & D/2 \\ B/2 & C & E/2 \\ D/2 & E/2 & F \end. == Classification == Regular and degenerate conic sections can be distinguished〔Lawrence, J. Dennis, ''A Catalog of Special Plane Curves'', Dover Publ., 1972.〕〔Spain, Barry, ''Analytical Conics'', Dover, 2007.〕〔Pettofrezzo, Anthony, ''Matrices and Transformations'', Dover, 1966.〕 based on the determinant of AQ. If $\backslash det\; A\_Q\; =\; 0$, the conic is degenerate. If ''Q'' is not degenerate, we can see what type of conic section it is by computing the minor $\backslash det\; A\_$ (that is, the determinant of the submatrix resulting from removing the last row and the last column of AQ): :$$ A_ = \begin 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「Matrix representation of conic sections」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.