Fall 2014

Symmetrizing the Matrix Multiplication Tensor

Tuesday, Dec. 15, 2015 9:00 am9:35 am PST

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Calvin Lab

I will consider the symmetrization of the matrix multiplication tensor. This is the cubic polynomial trace(A^3), where A is a n*n matrix. Its interest relies on the fact that the asymptotic exponent for its rank (when n goes to infinity) is the same than the constant omega which measures the complexity of matrix multiplication. On the other hand, a cubic polynomial is more tractable and allows more algebraic geometry tools.