This work formally introduces and starts investigating the structure of matrix polynomial algebra extensions a coefficient by (elementary) matrix-variables over ground ring in not necessary commuting variables. These subalgebras full rings show up noncommutative algebraic geometry. We carefully study their (one-sided or bilateral) noetherianity, obtaining precise lift Hilbert Basis Theorem when...

In this paper, we introduce a new geometric description of the manifolds matrices fixed rank. The starting point is Grassmann manifold Gr(Rk) linear subspaces dimension r<k in Rk, which avoids use equivalence classes. set equipped with an atlas, provides it structure analytic modeled on R(k?r)×r. Then, define atlas for Mr(Rk×r) full rank and prove that resulting principal bundle base typical...

This article investigates the notions of exposed points and (exposed) faces in matrix convex setting. Matrix finite dimensions were first defined by Kriel 2019. Here this notion is extended to sets infinite-dimensional vector spaces. Then a connection between extreme established: point ordinary if only it exposed. leads Krein-Milman type result for that due Straszewicz-Klee classical convexity:...

Functional logistic regression has been developed to forecast a binary response variable from a functional predictor. In order to fit this model, it is usual to assume that the functional observations and the parameter function of the model belong to a same finite space generated by a basis of functions. This consideration turns the functional model into a multiple logit model whose design matr...

We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: “For any matrix , where is an row-stochastic matrix, is a nonnegative rank-one row-stochastic matrix, and ! " , the second eigenvalue of has modulus # $&%'#( ) . Furthermore, if has at least two irreducible closed subs...

With recent advances in FPGA (Field Programmable Gate Array) technology it is now feasible to use these devices to build special purpose processors for floating point intensive applications that arise in scientific computing. FPGA provides programmable hardware that can be used to design custom hardware without the high-cost of traditional hardware design. In this talk we discuss two multi-proc...