Last Updated :2025/12/06

involutant

Noun
Japanese Meaning
(数学)w次正方行列MとNが与えられた場合、involutantとは、行列 {1, M, M², …, M^(w-1)} と {1, N, N², …, N^(w-1)} の各要素の積から生成されるw²個の行列に対して、スカラー係数の線形関数を立て、その線形関数をゼロにすることにより得られるw²個のスカラー方程式の結果(resultant)として定義される量を指す。
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行列 M と N に対する値は、1, M, M^2, …, M^{w-1} と 1, N, N^2, …, N^{w-1} を掛け合わせて得られる w^2 個の行列にスカラー係数を持つ線形関数を作用させ、それをゼロに等置して得られる w^2 個のスカラー方程式のリザルト(消去式)である。

plural

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(mathematics) Given two matrices M, N of order w, the involutant is the resultant of the w² scalar equations obtained by equating to zero a linear function with scalar coefficients of the w² matrices which result from multiplying 1, m m², ... mʷ⁻¹ into 1, n, n², ... nʷ⁻¹.

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involutant

The involutant of matrices M and N is the resultant of the w2 scalar equations obtained by equating to zero a linear function with scalar coefficients acting on the w2 matrices produced by multiplying 1, M, M2, …, M{w-1} into 1, N, N2, …, N{w-1}.

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The involutant of matrices M and N is the resultant of the w2 scalar equations obtained by equating to zero a linear function with scalar coefficients acting on the w2 matrices produced by multiplying 1, M, M2, …, M{w-1} into 1, N, N2, …, N{w-1}.

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