Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4601932 | Linear Algebra and its Applications | 2010 | 9 Pages |
Abstract
Let A=(aij)A=(aij) be an n×nn×n complex matrix. For any real μμ, define the polynomialPμ(A)=∑σ∈Sna1σ(1)⋯anσ(n)μℓ(σ),where ℓ(σ)ℓ(σ) is the number of inversions of the permutation σσ in the symmetric group SnSn. We analyze and establish a conjecture on the location of the zeros of Pμ(A)Pμ(A), when AA is a non-diagonal positive definite matrix. We prove the conjecture for the particular case when AA is a Jacobi matrix. Our proof is independent from known results, and uses a connection with orthogonal polynomials and chain sequences.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
C.M. da Fonseca,