Add to ORKGLet a nonsingular S ∈ Mn (C) be given. For A ∈ Mn (C), set φS (A) = S−1AT S. We say that A is φS symmetric if φS (A) = A; we say that A is φS orthogonal if A ∈ GLn and φS (A) = A−1; we say that A has a φS polar decomposition if A = UP for some φS orthogonal U and φS symmetric P. Suppose that S−T S is normal and −1 ∈/ σ S−T S. We determine conditions on A ∈ Mn (C) so that A can be written as a sum of two φS orthogonal matrices
AbstractLet A,S∈Mn(C) be given. Suppose that S is nonsingular and Hermitian. Then A is ΛS-orthogonal...
AbstractIn this work it is shown that certain interesting types of orthogonal system of subalgebras ...
AbstractMotivated by applications in the theory of unitary congruence, we introduce the factorizatio...
Let S ∈ Mn(C) be nonsingular such that S−T S is normal (that is, the cosquare of S is normal). Set φ...
Let a nonsingular S ∈ Mn (C) be given. For a nonsingular A ∈ Mn (C), set ψS (A) = S−1A−1S. We say th...
AbstractLet S∈Mn be nonsingular. We set ψS(A)=S-1A¯-1S for all nonsingular A∈Mn; a matrix A is calle...
AbstractLet F∈{R,C,H}. Let Un(F) be the set of unitary matrices in Mn(F), and let On(F) be the set o...
AbstractLet S∈Mn(R) be such that S2=I or S2=-I. For A∈Mn(C), define ϕS(A)=S-1ATS. We study ϕS-orthog...
AbstractWe show that every A∈MnZ2k-1 can be written as a sum of orthogonal matrices (QQT=QTQ=I) in M...
For $S \in GL_n$, define $\phi_S: M_n \rightarrow M_n$ by $\phi_S(A) = S^{-1}A^TS$. A matrix $A \in ...
AbstractThe paper deals with those orthogonal matrices which can be expressed as linear combinations...
By a ∗-subalgebra of the matrix algebra Mn(C) we mean a subalgebra containing the identity closed un...
AbstractGiven a symmetric n × n matrix A and n numbers r1,…,rn, necessary and sufficient conditions ...
Literature to this topic: [1–4]. x†y ⇐⇒< y,x>: standard inner product. x†x = 1: x is normalize...
AbstractLet A and B be rectangular matrices. Then A is orthogonal to B if∥A+μB∥⩾∥A∥foreveryscalarμ.S...
AbstractLet A,S∈Mn(C) be given. Suppose that S is nonsingular and Hermitian. Then A is ΛS-orthogonal...
AbstractIn this work it is shown that certain interesting types of orthogonal system of subalgebras ...
AbstractMotivated by applications in the theory of unitary congruence, we introduce the factorizatio...
Let S ∈ Mn(C) be nonsingular such that S−T S is normal (that is, the cosquare of S is normal). Set φ...
Let a nonsingular S ∈ Mn (C) be given. For a nonsingular A ∈ Mn (C), set ψS (A) = S−1A−1S. We say th...
AbstractLet S∈Mn be nonsingular. We set ψS(A)=S-1A¯-1S for all nonsingular A∈Mn; a matrix A is calle...
AbstractLet F∈{R,C,H}. Let Un(F) be the set of unitary matrices in Mn(F), and let On(F) be the set o...
AbstractLet S∈Mn(R) be such that S2=I or S2=-I. For A∈Mn(C), define ϕS(A)=S-1ATS. We study ϕS-orthog...
AbstractWe show that every A∈MnZ2k-1 can be written as a sum of orthogonal matrices (QQT=QTQ=I) in M...
For $S \in GL_n$, define $\phi_S: M_n \rightarrow M_n$ by $\phi_S(A) = S^{-1}A^TS$. A matrix $A \in ...
AbstractThe paper deals with those orthogonal matrices which can be expressed as linear combinations...
By a ∗-subalgebra of the matrix algebra Mn(C) we mean a subalgebra containing the identity closed un...
AbstractGiven a symmetric n × n matrix A and n numbers r1,…,rn, necessary and sufficient conditions ...
Literature to this topic: [1–4]. x†y ⇐⇒< y,x>: standard inner product. x†x = 1: x is normalize...
AbstractLet A and B be rectangular matrices. Then A is orthogonal to B if∥A+μB∥⩾∥A∥foreveryscalarμ.S...
AbstractLet A,S∈Mn(C) be given. Suppose that S is nonsingular and Hermitian. Then A is ΛS-orthogonal...
AbstractIn this work it is shown that certain interesting types of orthogonal system of subalgebras ...
AbstractMotivated by applications in the theory of unitary congruence, we introduce the factorizatio...