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Joseph Fehribach (WPI)-Matrices and Their Kirchhoff Graphs

Mathematics - Colloquium

Friday, November 30, 2012
11:00 AM-12:00 PM

Salisbury Laboratories
105

ABSTRACT: Given a matrix with integer or rational elements, what graph or graphs represent this matrix in terms of the fundamental theorem of linear algebra (that the row space and the null space of a matrix are orthogonal complements)? This talk will define the concept of a Kirchhoff or fundamental graph for the matrix and will explain how such a graph represents a matrix. A number of basic results pretaining to Kirchhoff graphs will be presented and a process for constructing them will be discussed. Finally the talk will conclude with an example from electrochemistry: the production of NaOH from NaCl. Kirchhoff graphs have their origin in electrochemical reaction networks and are closely related to reaction route graphs.

This talk will be a follow-up to my previous talk given at WPI in September, 2008; it will concentrate on results achieved since that time.

Suggested Audiences: Adult, College

E-mail: ma-chair@wpi.edu

Last Modified: November 29, 2012 at 2:58 PM

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