AbstractLet dn[dn(r)] denote the codimension of the set of pairs of n×n Hermitian [really symmetric] matrices (A, B) for which det(λI−A−xB)=p(λ,x) is a reducible polynomial. We prove that dn(r)⩽n−1, dn⩽n−1 (n odd), dn⩽n (n even). We conjecture that the equality holds in all three inequalities. We prove this conjecture for n=2,3
Abstract. The set of all solutions to the homogeneous system of matrix equations (XTA + AX,XTB +BX) ...
AbstractGiven two monic polynomials P2n and P2n−2 of degree 2n and 2n−2 (n⩾2) with complex coefficie...
AbstractLet A − λB be a definite matrix pencil of order n, i.e., both A and B are n × n Hermitian an...
Let A be an n × n complex matrix, and write A = H + iK, where i² = −1 and H and K are Hermitian matr...
AbstractLet A be an n × n complex matrix, and write A = H + iK, where i2 = −1 and H and K are Hermit...
Let A be an n × n matrix; write A = H+iK, where i² = —1 and H and K are Hermitian. Let f(x,y,z) = de...
Abstract. A standard way of treating the polynomial eigenvalue problem P (λ)x = 0 is to convert it i...
Let A be an n × n complex matrix and write A = H + iK, where H and K are Hermitian matrices. We show...
AbstractLet A be an n × n complex matrix and write A = H + iK, where H and K are Hermitian matrices....
AbstractA counterexample is constructed to a conjecture of Kippenhahn (Math. Nachr. 6:193–288 (1951–...
Abstract. A standard way of treating the polynomial eigenvalue problem P (λ)x = 0 is to convert it i...
A standard way of treating the polynomial eigenvalue problem $P(\l)x = 0$ is to convert it into an e...
AbstractAn essential subproblem in the study of invariants of homogeneous matrix pencils sF − ŝG und...
We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are con...
AbstractLet F be an arbitrary field, H be a subgroup of the symmetric group of degree m, Sm, λ be an...
Abstract. The set of all solutions to the homogeneous system of matrix equations (XTA + AX,XTB +BX) ...
AbstractGiven two monic polynomials P2n and P2n−2 of degree 2n and 2n−2 (n⩾2) with complex coefficie...
AbstractLet A − λB be a definite matrix pencil of order n, i.e., both A and B are n × n Hermitian an...
Let A be an n × n complex matrix, and write A = H + iK, where i² = −1 and H and K are Hermitian matr...
AbstractLet A be an n × n complex matrix, and write A = H + iK, where i2 = −1 and H and K are Hermit...
Let A be an n × n matrix; write A = H+iK, where i² = —1 and H and K are Hermitian. Let f(x,y,z) = de...
Abstract. A standard way of treating the polynomial eigenvalue problem P (λ)x = 0 is to convert it i...
Let A be an n × n complex matrix and write A = H + iK, where H and K are Hermitian matrices. We show...
AbstractLet A be an n × n complex matrix and write A = H + iK, where H and K are Hermitian matrices....
AbstractA counterexample is constructed to a conjecture of Kippenhahn (Math. Nachr. 6:193–288 (1951–...
Abstract. A standard way of treating the polynomial eigenvalue problem P (λ)x = 0 is to convert it i...
A standard way of treating the polynomial eigenvalue problem $P(\l)x = 0$ is to convert it into an e...
AbstractAn essential subproblem in the study of invariants of homogeneous matrix pencils sF − ŝG und...
We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are con...
AbstractLet F be an arbitrary field, H be a subgroup of the symmetric group of degree m, Sm, λ be an...
Abstract. The set of all solutions to the homogeneous system of matrix equations (XTA + AX,XTB +BX) ...
AbstractGiven two monic polynomials P2n and P2n−2 of degree 2n and 2n−2 (n⩾2) with complex coefficie...
AbstractLet A − λB be a definite matrix pencil of order n, i.e., both A and B are n × n Hermitian an...
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