TY - JOUR
T1 - Cofactors and eigenvectors of banded Toeplitz matrices
T2 - Trench formulas via skew Schur polynomials
AU - Maximenko, Egor A.
AU - Moctezuma-Salazar, Mario Alberto
N1 - Publisher Copyright:
© 2017, Element D.O.O. All rights reserved.
PY - 2017/12
Y1 - 2017/12
N2 - The Jacobi–Trudi formulas imply that the minors of the banded Toeplitz matrices can be written as certain skew Schur polynomials. In 2012, Alexandersson expressed the corresponding skew partitions in terms of the indices of the struck-out rows and columns. In the present paper, we develop the same idea and obtain some new applications. First, we prove a slight generalization and modification of Alexandersson’s formula. Then, we deduce corollaries about the cofactors and eigenvectors of banded Toeplitz matrices, and give new simple proofs to the corresponding formulas published by Trench in 1985.
AB - The Jacobi–Trudi formulas imply that the minors of the banded Toeplitz matrices can be written as certain skew Schur polynomials. In 2012, Alexandersson expressed the corresponding skew partitions in terms of the indices of the struck-out rows and columns. In the present paper, we develop the same idea and obtain some new applications. First, we prove a slight generalization and modification of Alexandersson’s formula. Then, we deduce corollaries about the cofactors and eigenvectors of banded Toeplitz matrices, and give new simple proofs to the corresponding formulas published by Trench in 1985.
KW - Cofactor
KW - Eigenvector
KW - Minor
KW - Skew Schur function
KW - Toeplitz matrix
UR - http://www.scopus.com/inward/record.url?scp=85035061282&partnerID=8YFLogxK
U2 - 10.7153/oam-2017-11-79
DO - 10.7153/oam-2017-11-79
M3 - Artículo
SN - 1846-3886
VL - 11
SP - 1149
EP - 1169
JO - Operators and Matrices
JF - Operators and Matrices
IS - 4
ER -