Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem.
(Homogeneous) Markov bridges are (time homogeneous) Markov chains which begin at a given point and end at a given point. The price to pay for preserving the homogeneity is to work with processes with a random life-span. Bridges are studied both for themselves and for their use in describing the transformations of Markov chains: restriction on a random interval, time reversal, time change, various conditionings comprising the confinement in some part of the state space. These bridges lead us to look...
Let be the multiplicative semigroup of all complex matrices, and let and be the –degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from to when or , and thereby determine multiplicative homomorphisms from to when or . This generalize Hochwald’s result in [Lin. Alg. Appl. 212/213:339-351(1994)]: if is a spectrum–preserving multiplicative homomorphism, then there exists a matrix in such that for...