In this chapter we study polynomials with quaternion matrix coeffcients. The exposition is focused on two major results. One is the Smith form, which asserts that every quaternion matrix polynomial can be brought to a diagonal form under pre- and postmultiplication by unimodular matrix polynomials, with the appropriate divisibility relations among the diagonal entries. The other is the Kronecker canonical form for quaternion matrix polynomials of first degree under pre- and postmultiplication by invertible constant matrices. The Kronecker form generalizes the Jordan canonical for matrices. Complete and detailed proofs are given for both the Smith form and the Kronecker form.

EP - 171 PB - Princeton University Press PY - 2014 SN - 9780691161853 SP - 153 T2 - Topics in Quaternion Linear Algebra UR - http://www.jstor.org/stable/j.ctt6wpz0p.10 Y2 - 2021/09/23/ ER -