Zonal Polynomials of the Real Positive Definite Symmetric Matrices

1961 ◽  
Vol 74 (3) ◽  
pp. 456 ◽  
Author(s):  
Alan T. James
Keyword(s):  
Positive Definite ◽  
Symmetric Matrices ◽  
Zonal Polynomials ◽  
The Real

The Inverse Eigenvalue Problem for Symmetric Doubly Arrow Matrices

2013 ◽  
Vol 444-445 ◽  
pp. 625-627
Author(s):  
Kan Ming Wang ◽  
Zhi Bing Liu ◽  
Xu Yun Fei
Keyword(s):  
Eigenvalue Problem ◽  
Special Kind ◽  
Inverse Eigenvalue Problem ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Real ◽  
Inverse Eigenvalue ◽  
Necessary And Sufficient

In this paper we present a special kind of real symmetric matrices: the real symmetric doubly arrow matrices. That is, matrices which look like two arrow matrices, forward and backward, with heads against each other at the station, . We study a kind of inverse eigenvalue problem and give a necessary and sufficient condition for the existence of such matrices.

scholarly journals Identification of the theory of orthogonal polynomials in d-indeterminates with the theory of 3-diagonal symmetric interacting Fock spaces on ℂd

2017 ◽  
Vol 20 (01) ◽  
pp. 1750004 ◽  
Author(s):  
Luigi Accardi ◽  
Abdessatar Barhoumi ◽  
Ameur Dhahri
Keyword(s):  
Orthogonal Polynomials ◽  
Polynomial Algebra ◽  
Random Variables ◽  
Positive Definite ◽  
Probability Measures ◽  
Fock Spaces ◽  
Positive Definite Kernels ◽  
Algebraic Classification ◽  
The Real

The identification mentioned in the title allows a formulation of the multidimensional Favard lemma different from the ones currently used in the literature and which parallels the original 1-dimensional formulation in the sense that the positive Jacobi sequence is replaced by a sequence of positive Hermitean (square) matrices and the real Jacobi sequence by a sequence of positive definite kernels. The above result opens the way to the program of a purely algebraic classification of probability measures on [Formula: see text] with moments of any order and more generally of states on the polynomial algebra on [Formula: see text]. The quantum decomposition of classical real-valued random variables with all moments is one of the main ingredients in the proof.

scholarly journals Generalized Laplace transform with matrix variables

1987 ◽  
Vol 10 (3) ◽  
pp. 503-511
Author(s):  
R. M. Joshi ◽  
J. M. C. Joshi
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Hankel Transform ◽  
Laplace Transforms ◽  
Confluent Hypergeometric Function ◽  
Symmetric Matrices ◽  
The Real ◽  
Matrix Argument ◽  
Alpha Beta

In the present paper we have extended generalized Laplace transforms of Joshi to the space ofm×msymmetric matrices using the confluent hypergeometric function of matrix argument defined by Herz as kernel. Our extension is given byg(z)=Γm(α)Γm(β)∫∧>01F1(α:β:−∧z) f(∧)d∧The convergence of this integral under various conditions has also been discussed. The real and complex inversion theorems for the transform have been proved and it has also been established that Hankel transform of functions of matrix argument are limiting cases of the generalized Laplace transforms.

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