Poles and zeros of matrices of rational functions

AbstractThis expository paper considers the problem of defining poles and zeros with multiplicity, including those at infinity, for a matrix of rational functions over a field. The underlying theme question for the paper is: does the number of poles of a matrix equal the number of zeros, and what structural meaning underlies such an assertion? Our approach is motivated by ideas from linear system theory and control engineering. Control-theoretic ideas are not a prerequisite, and we hope to encourage specialists in classical linear and commutative algebra to investigate this promising source of new algebra problems