Trace Diagrams, Matrix Minors, and Determinant Identities
Combinatorics
2010-11-30 v2
Abstract
Trace diagrams are structured graphs with edges labeled by matrices. Each diagram has an interpretation as a particular multilinear function. We provide a rigorous combinatorial definition of these diagrams using a notion of signed graph coloring, and prove that they may be efficiently represented in terms of matrix minors. Using this viewpoint, we provide new proofs of several standard determinant formulas and a new generalization of the Jacobi determinant theorem.
Cite
@article{arxiv.0903.1373,
title = {Trace Diagrams, Matrix Minors, and Determinant Identities},
author = {Steven Morse and Elisha Peterson},
journal= {arXiv preprint arXiv:0903.1373},
year = {2010}
}
Comments
This updated version includes significantly expanded proofs and a new generalization of the Jacobi determinant theorem