This paper studies necessary and sufficient conditions for
a matrix to be conjunctive with its adjoint. The problem is solved
completely in the usual complex case, in which it is shown that a
matrix is conjunctive to its adjoint iff it is conjunctive to a real
matrix. The problem is...
In this thesis we define two nxn matrices T and S to be isoconjunctive if there exists an nxn nonsingular hermitian matrix H such that T = HSH. We then proceed to establish necessary and sufficient conditions that two nxn matrices T and S be isoconjunctive in the case where...
Computing eigenpairs of a matrix corresponding to a specific geometry in the complex plane is an important topic in real time signal processing, pattern recognition, spectral analysis, systems theory, radar, sonar, and geophysics. We have studied the matrix sign and matrix sector function iterations to extract the eigenpairs belonging to...
In this work, we study network coding technique, its relation to random matrices, and their applications to communication systems. The dissertation consists of three main contributions. First, we propose efficient algorithms for data synchronization via a broadcast channel using random network coding. Second, we study the resiliency of network coding...