A polynomial time spectral decomposition test for certain classes of inverse M-matrices
نویسندگان
چکیده
The primary result in this paper is a set of O(n) time algorithms to determine whether a speci ed real, symmetric matrix is a member of any of several closely related classes: the MMA-matrices; the inverse MMA-matrices; the strictly positive, positive de nite matrices whose eigenvectors form a Soules basis; and the strictly ultrametric matrices. When the class membership question is answered in the a rmative for anMMA-matrix or an inverseMMA-matrix, the algorithms also yield the complete spectral decomposition of the matrix in question. Additional results in this paper include an algorithmic test for when a matrix is a Soules matrix, and a construction for Soules bases. AMS subject classi cations. 15A48, 15A18
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