Generalized reflexive and anti-reflexive solution for a system of equations
نویسندگان
چکیده
منابع مشابه
Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$. An $ntimes n$ complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$). In this paper, we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...
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Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., R = R = R−1 = ±Im and S = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize ‖AX−Z‖2+‖Y HA−WH‖2, a...
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a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$. an $ntimes n$ complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$). in this paper, we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...
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Let n n complex matrices P andQ be nontrivial generalized reflection matrices, i.e., P D P D P 1 ¤ In, Q DQ DQ 1 ¤ In. A complex matrix A with order n is said to be a .P;Q/ generalized anti-reflexive matrix, if PAQ D A. We in this paper mainly investigate the .P;Q/ generalized anti-reflexive maximal and minimal rank solutions to the system of matrix equation AX D B . We present necessary and su...
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Linear matrix equations play an important role in many areas, such as control theory, system theory, stability theory and some other fields of pure and applied mathematics. In the present paper, we consider the generalized coupled Sylvestertranspose and conjugate matrix equations Tν(X) = Fν , ν = 1, 2, . . . , N, where X = (X1, X2, . . . , Xp) is a group of unknown matrices and for ν = 1, 2, . ...
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ژورنال
عنوان ژورنال: Filomat
سال: 2016
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1601055n