论文信息 - A - Lower Bound for the Rank of - Matrix Multiplication over Arbitrary Fields

A - Lower Bound for the Rank of - Matrix Multiplication over Arbitrary Fields

We prove a lower bound of \math for the rank of \math 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.

M. Bläser

[1] K. Ramachandra,et al. Vermeidung von Divisionen. , 1973 .

[2] David P. Dobkin,et al. On the optimal evaluation of a set of bilinear forms , 1978 .

[3] Hans F. de Groote. On Varieties of Optimal Algorithms for the Computation of Bilinear Mappings I. The Isotropy Group of a Bilinear Mapping , 1978, Theor. Comput. Sci..

[4] Volker Strassen,et al. On the Algorithmic Complexity of Associative Algebras , 1981, Theor. Comput. Sci..

[5] V. Strassen. Rank and optimal computation of generic tensors , 1983 .

[6] Jacques Morgenstern,et al. On associative algebras of minimal rank , 1984, International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes.

[7] Hans F. de Groote. Lectures on the Complexity of Bilinear Problems , 1987, Lecture Notes in Computer Science.

[8] Nader H. Bshouty. A Lower Bound for Matrix Multiplication , 1989, SIAM J. Comput..

[9] Don Coppersmith,et al. Matrix multiplication via arithmetic progressions , 1987, STOC.

[10] Michael Clausen,et al. Algebraic complexity theory , 1997, Grundlehren der mathematischen Wissenschaften.

[11] Markus Bläser. Lower bounds for the multiplicative complexity of matrix multiplication , 1999, computational complexity.