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It was mainly due to Atkinson works, who introduced Linear Multiparameter Eigenvalue problems (LMEPs), based on determinantal operators on the Tensor Product Space. Later, in the area of Multiparameter eigenvalue problems has received attention from the Mathematicians in the recent years also, who pointed out that there exist a variety of mixed eigenvalue problems with several parameters in different scientific domains. This article aims to bring into a light variety of scientific problems that appear naturally as LMEPs. Of course, with all certainty, the list of collection of applications presented here are far from complete, and there are bound to be many more applications of which we are currently unaware. The paper may provide a review on applications of Multiparameter eigenvalue problems in different scientific domains and future possible applicatios both in theoretical and applied disciplines.

Computation of antieigenvalue and its corresponding antieigenvetors of matrices have received attention by the researcher in recent years. In this paper, a unified framework for generalized antieigenvalue pair of linear two-parameter matrix eigenvalue problems (LTMEPs) are discussed. An upper bound of generalized antieigenvalue pair is estimated in terms of numerical range of certain pair operator matrices.