𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Algebraic Aspects of Matrix Orthogonality for Vector Polynomials

✍ Scribed by Vladimir N. Sorokin; Jeannette Van Iseghem

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
355 KB
Volume
90
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

An algebraic theory of orthogonality for vector polynomials with respect to a matrix of linear forms is presented including recurrence relations, extension of the Shohat Favard theorem, of the Christoffel Darboux formula, and its converse. The connection with orthogonal matrix polynomials is described.

πŸ“œ SIMILAR VOLUMES

New Automorphisms of Generic Matrix Alge
New Automorphisms of Generic Matrix Algebras and Polynomial Algebras
✍ Vesselin Drensky; C.K. Gupta πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 148 KB

Let T be the generic trace algebra generated by the algebra R of two generic 2 = 2 matrices and by all traces of the matrices from R over a field K. We construct new automorphisms of T and R. They induce automorphisms of the polynomial algebra in five variables which fix two of the variables. Our au

Commutant Algebra and Harmonic Polynomia
Commutant Algebra and Harmonic Polynomials of the Lie Algebra of Vector Fields
✍ Kyo Nishiyama πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 199 KB

We determine the commutant algebra of W in the m-fold tensor product of its n natural representation in the case m F n. For m ) n, we show that the commutant algebra is of finite dimension by introducing a new kind of harmonic polynomial.