English Dictionary

multilinear form

名詞

広義

(linear algebra, multilinear algebra) Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;

日本語の意味

多線形形式：ベクトル空間Vのk個の元を体Kの元に写す写像で、各引数に対して線形性を持つもの。 / 多変数線形写像：各引数について線形な性質を示す関数。

To compute the determinant, one can interpret it as a multilinear form on the rows of a matrix that changes sign under row swaps.

行列式を計算するには、それを行列の行に作用する各引数ごとに線形なスカラー値への写像（多重線形形式）として解釈でき、行の入れ替えで符号が変わる。

意味（1）

(linear algebra, multilinear algebra) Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;

Finally, in the short Lecture 5 we make some remarks on multilinear forms over Hilbert spaces, a theory which is still in a rather embryonic state, motivated by the observation that paracommutators (and Hankel operators too) really should be viewed as forms, not operators.

意味（2）

(more generally) a similarly multiply linear mapping Mʳ → R defined for a given module M over some commutative ring R.

multilinear forms （ plural ）