Equations for Lower Bounds on Border Rank Academic Article

abstract

• We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r=6 in the space of bilinear maps. This space of bilinear maps includes the matrix multiplication operator M2 for 22 matrices. We show that these newly obtained polynomials do not vanish on the matrix multiplication operator M2, which gives a new proof that the border rank of the multiplication of 22 matrices is seven. Other examples are considered along with an explanation of how to implement the methods. 2013 Copyright Taylor and Francis Group, LLC.

authors

• Landsberg, Joseph

published proceedings

• EXPERIMENTAL MATHEMATICS

author list (cited authors)

• Hauenstein, J. D., Ikenmeyer, C., & Landsberg, J. M.

citation count

• 16

complete list of authors

• Hauenstein, Jonathan D||Ikenmeyer, Christian||Landsberg, JM

publication date

• January 2013

publisher

• Taylor & Francis  Publisher

published in

• Experimental Mathematics  Journal

keywords

• Border Rank
• Matrix Multiplication

Digital Object Identifier (DOI)

• 10.1080/10586458.2013.825892

start page

• 372

end page

• 383

volume

• 22

issue

• 4

URL

• http://dx.doi.org/10.1080/10586458.2013.825892