When these two matrix equations are consistent, the convergence theorem shows that a solution can be obtained within finite iterative steps in the absence of round-off error for any initial arbitrary Hermitian R R mathContainer Loading Mathjax -conjugate solution matrices V 1 V 1 mathContainer ...
Let P∈Cm×m and Q∈Cn×n be Hermitian and {k+1}-potent matrices,i.e.,Pk+1=P=P*,Qk+1=Q=Q*,where(·)* stands for the conjugate transpose of a matrix.A matrix X∈Cm×n is called {P,Q,k+1}-reflexive(anti-reflexive) if PXQ=X(PXQ=-X).In this ... 董昌州,李浩雪 - 《...
(B4Y ) - A4XA* 4; where C4 is Hermitian,* denotes the conjugate transpose, X and Y satisfy the following consistent system of matrix equations A3Y = C3;A1X = C1,XB1 = D1,A2XA*2 = C2,X = X* As consequences, we get the necessary and sufficient conditions for the above ...
The iterative method of the generalized coupled Sylvester-conjugate matrix equations over Hermitian and generalized skew Hamiltonian solution is presented. When these systems of matrix equations are consistent, for arbitrary initial Hermitian and generalized skew Hamiltonian matrices X (j) (1), j = 1,...
By proper formulation of a step in the factorization algorithm of an elementary paraconjugate Hermitian polynomial matrix the exponential time-bound can be reduced to low polynomial one. As the remaining steps have polynomial time-bound a big save is expected in larger problems. The reduction is ...
From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ(𝑡)Θ(t) is made redundant. The implementation of the...
For the reasons explained in the related literature [20], one must add also the information about the metric or, equivalently, about the second ket-vector |𝜓(𝑡)〉〉∈ℋ(𝐹)|ψ(t)〉〉∈H(F), with its time-evolution controlled by the other, conjugate, independent ...