Theory and Applications of Matrices Described by Patterns (10w5024)


(University of Wisconsin - Madison)

Shaun Fallat (University of Regina)

(Iowa State University)

(University of Wyoming)

(University of Victoria)


The Banff International Research Station will host the "Theory and Applications of Matrices Described by Patterns" workshop from January 31st to February 5th, 2010.

Solving systems of equations is at the heart of many mathematical endeavors. For equations that describe lines, planes and so-on (linear equations), the fundamental object is an array of numbers (representing the coefficients of the equations), which is known as a matrix. The solvability of these equations often relies on the amount of information that can be retrieved from the relevant data. For example, if the actual coefficients are unknown, but the positions of the nonzero coefficients (or the signs of the coefficients) are known, this information can be used to deduce properties about the system of equations.

The purpose of this workshop is to investigate properties of the corresponding matrices when only combinatorial (position or sign) data is used. For example, we ask questions about minimum rank (and other important properties) when the pattern of nonzero entries is given, and we ask the same questions assuming we know where the zero, positive and negative entries are specified.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).