# Differences

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 multilinear_functional [2013/08/31 18:44]nikolaj created multilinear_functional [2014/03/21 11:11] (current) 2013/08/31 19:34 nikolaj 2013/08/31 18:44 nikolaj created Next revision Previous revision 2013/08/31 19:34 nikolaj 2013/08/31 18:44 nikolaj created Line 1: Line 1: - ===== Multilinear functional ​ ===== + ===== Multilinear functional ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $X$...$\mathcal F$-vector space | + | @#55CCEE: context ​    | @#55CCEE: $X$...$\mathcal F$-vector space | - | @#88DDEE: $n\in \mathbb N$ | + | @#55CCEE: context ​    | @#55CCEE: $n\in \mathbb N$ | - | @#FFBB00: $M\in \mathrm{MultiLin}(X^n)$ | + | @#FFBB00: definiendum ​| @#FFBB00: $M\in \mathrm{MultiLin}(X^n)$ | - | @#88DDEE: $M:X^n \to \mathcal F$ | + | @#55CCEE: context ​    | @#55CCEE: $M:X^n \to \mathcal F$ | $X^n$ being the cartesian product of $n$ instances of the vector space $X$. $X^n$ being the cartesian product of $n$ instances of the vector space $X$. Line 14: Line 14: | $1\le j\le n$ | | $1\le j\le n$ | - | @#55EE55: $M(v_1,​\dots,​a\cdot v_j+b\cdot w,​\dots,​v_n)=a\ M(v_1,​\dots,​v_j,​\dots,​v_n)+b\ M(v_1,​\dots,​w,​\dots,​v_n)$ | + | @#55EE55: postulate ​  | @#55EE55: $M(v_1,​\dots,​a\cdot v_j+b\cdot w,​\dots,​v_n)=a\ M(v_1,​\dots,​v_j,​\dots,​v_n)+b\ M(v_1,​\dots,​w,​\dots,​v_n)$ | ==== Discussion ==== ==== Discussion ==== - ==== Context ​==== + ==== Parents ​==== === Subset of === === Subset of === [[Function]] [[Function]] - === Requirements ​=== + === Context ​=== [[Vector space]] [[Vector space]]