The resultant for regular matrix polynomials and quasi commutativity I. GohbergM. KaashoekL. Lerer 15A0615A0915A2415A1547A56matrix polynomialsmatrix polynomial equationsquasi-commutativitycommon eigenvaluescommon spectral datablock resultant matrices of square size Necessary and sufficient conditions are presented in order that for two regular matrix polynomials the null space of the straightforward analogue of the classical Sylvester resultant matrix is completely determined by the common spectral data of the polynomials involved. The conditions are stated in terms of a quasi commutativity property. In the scalar case, and more generally in the case of commuting matrix polynomials, the conditions are automatically satisfied. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3698 10.1512/iumj.2008.57.3698 en Indiana Univ. Math. J. 57 (2008) 2793 - 2814 state-of-the-art mathematics http://iumj.org/access/