We present a new minimal residual method, called global R-linear GMRES, to solve the R-linear matrix equations X + AXB = C and X + AXB = C, where C, X ∈ Cm×n, X denotes the complex conjugate of X, X its complex conjugate transpose, and A, B are complex matrices with appropriate dimensions. We show that the new method requires fewer matrix-matrix products than the global GMRES method applied to ...

Let R be an n by n nontrivial real symmetric involution matrix, that is, R R−1 R / In. An n × n complex matrix A is termed R-conjugate if A RAR, where A denotes the conjugate of A. We give necessary and sufficient conditions for the existence of the Hermitian R-conjugate solution to the system of complex matrix equations AX C andXB D and present an expression of the Hermitian R-conjugate soluti...

As usual, R denotes the field of real numbers, R" stands for the n-dimensional vector space over R, a prime denotes the transpose of a matrix, an asterisk denotes the complex conjugate transpose of a matrix, and P _ Q means that P — Q is hermitian or real symmetric nonnegative matrix. Square brackets represent matrices composed of the symbols inside. In order to get a better motivation for the ...

Let G be a finite group and let h positive integer. A BH(G, h) matrix is G-invariant ∣G∣ × H whose entries are complex hth roots of unity such that H* = ∣G∣I∣G∣, where denotes the conjugate transpose H, I∣G∣ identity order ∣G∣. In this paper, we give three new constructions matrices. The first construction known family matrices in which does not need to abelian. second third two families local ...

The Dold manifold P (m,n) is obtained from the product Sm × CPn of the m-dimensional sphere and n-dimensional complex projective space by identifying (x, [z1, . . . , zn+1]) with (−x, [z̄1, . . . , z̄n+1]), where z̄ denotes the complex conjugate of z. We answer the parallelizability question for the Dold manifolds P (m,n) and, by completing an earlier (2008) result due to Peter Novotný, we solve t...