一个5/2n/sup 2/-下界n/spl乘以任意域上的/n矩阵乘法的秩

40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039) Pub Date : 1999-10-17 DOI:10.1109/SFFCS.1999.814576

M. Blaser

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引用次数: 34

摘要

我们证明了任意域上n/spl乘以/n矩阵乘法的秩的下界为5/2n/sup 2/-3n。对于非交换除法代数中乘法的秩和上三角矩阵的乘法也有类似的界。

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A 5/2n/sup 2/-lower bound for the rank of n/spl times/n-matrix multiplication over arbitrary fields

We prove a lower bound of 5/2n/sup 2/-3n for the rank of n/spl times/n-matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.

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40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)

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