The existence of left eigenvalues for quaternionic matrix

摘要

In this work, an algebraic method to prove the existence of left eigenvalues for the quaternionic matrix is investigated. The left eigenvalues of a n×n quaternionic matrix can be derived by solving the zeros of a general quaternionic polynomial of degree 2n. Using the Study’s determinant, it can be found by solving the zeros of quaternionic polynomials of degree at most n or of rational functions.