In response to a question posed by João P. Silva, I demonstrate that an arbitrary 2n×2n real orthogonal antisymmetric matrix can be parameterized by n(n−1) continuous angular parameters. An algorithm is provided for constructing the general form for such a matrix. This algorithm is based on observation that Sp(n,R) ∩ O(2n) ∼= U(n) and employs the parameterization of the coset space SO(2n)/U(n)....

We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists Jacobi scalar factor and part. Using Riemann–Hilbert formulation for MVOPs Deift–Zhou method steepest descent, we obtain expansions as tends to infinity, in different regions complex plane (outside interval orthogonality, on away from endpoints neighborhoods endpoints), w...

In this paper, we study a class of matrix-valued orthogonal polynomials (MVOPs) that are related to 2-periodic lozenge tilings hexagon. The general model depends on many parameters. the cases constant and parameter values show MVOP can be expressed in terms scalar with non-Hermitian orthogonality closed contour complex plane. hexagon tiling has phase transition large size limit. This is reflect...

This paper shows that Cayley Transforms, which map Orthogonal and SkewSymmetric matrices, may be considered the extension to matrix field of the complex conformal mapping function f1(z) = 1− z 1 + x . Then, by using a set of real matrices which are, simultaneously, Orthogonal and Symmetric (the Ortho−Sym matrices), it similarly shows how to extend two complex conformal mapping functions (namely...