A polarization identity for multilinear maps
A polarization identity for multilinear maps
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多线性映射的极化恒等式
DOI：
10.1016/j.indag.2013.11.003
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
E. Thomas
中科院分区：
文献类型：
--
作者：
E. Thomas
给定真实的数上的线性空间E和F或特征为零的域，给出一个简单的论证，表示从En到F的对称多线性映射u（x1，x2，.，xn）对对角线的限制.作为应用，推导出了纳尔逊和谢岑所用的高斯变量的概率表达式。汤姆·H的附录Koornwinder注意到Bochnak和Siciak（1971）对主要结果的证明进行了进一步的简化。
Given linear spaces E and F over the real numbers or a field of characteristic zero, a simple argument is given to represent a symmetric multilinear map u (x 1, x 2,…, x n) from E n to F in terms of its restriction to the diagonal. As an application, a probabilistic expression for Gaussian variables used by Nelson and by Schetzen is derived. An Appendix by Tom H. Koornwinder notes an even further simplification by Bochnak and Siciak (1971) of the proof of the main result.