Positive Semi-Definite Matrices and Hilbert spaces
Using functional analysis, operator theory, frame theory, harmonic analysis, matrix analysis, function theory, and dynamical systems, research is conducted on positive semi-definite matrices and Hilbert spaces.
Positive semi-definite matrices arise in various basic sciences, engineering, and operations research applications. Copositive matrices, semimonotone matrices, and other generalizations like P0-matrices of positive semi-definite matrices play a significant role in the theory of linear complementarity problem (LCP). We aim to exploit the LCP theory to characterize these matrix classes with the motivation further that these characterizations will be highly useful not only in optimization theory but also in the applications like block designs, data mining and clustering, a model of energy demand, exchangeable probability distributions, and in dynamical systems and control.
- Dr. Sneh Lata, Asst. Professor
- Dr. Dipti Dubey, Assistant Professor