• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.409-418
• /
• 2016

In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.

• East Asian mathematical journal
• /
• v.38 no.1
• /
• pp.95-105
• /
• 2022

In this paper, we consider a quadratic matrix equation Q(X) = AX² + BX + C = 0 where A, B, C ∈ ℝ^n×n. A new approach is proposed to find solutions of Q(X), using the novel structure of the information processing system. We also present some numerical experimetns with Artificial Neural Network.

• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1055-1073
• /
• 2018

In this paper, we define an alternative q-analogue of the $Ruci{\acute{n}}ski$-Voigt numbers. We obtain fundamental combinatorial properties such as recurrence relations, generating functions and explicit formulas which are shown to be q-deformations of similar properties for the $Ruci{\acute{n}}ski$-Voigt numbers, and are generalizations of the results obtained by other authors. A combinatorial interpretation in the context of A-tableaux is also given where convolution-type identities are consequently obtained. Lastly, we establish the matrix decompositions of the $Ruci{\acute{n}}ski$-Voigt and the q-$Ruci{\acute{n}}ski$-Voigt numbers.

• Journal of Mechanical Science and Technology
• /
• v.17 no.3
• /
• pp.329-335
• /
• 2003

EALQR (Linear Quadratic Regulate. design with Eigenstructure Assignment capability) has the capability of exact assignment of eigenstructure with the guaranteed margins of the LQR for MIMO (Multi-Input Multi-Output) systems. However, EALQR undergoes a restriction on the state-weighting matrix Q in LQR to be indefinite with respect to the region of allowable closedloop eigenvalues. The definiteness of the weighting matrix is closely related to the robustness property of a given system. In this paper, we derive a relation between the indefinite weighting matrix Q and the robustness property for EALQR. The modified frequency domain inequality, that could be guaranteed by EQLQR with an indefinite weighting matrix, is presented.

• East Asian mathematical journal
• /
• v.28 no.5
• /
• pp.587-595
• /
• 2012

In this paper we consider the quadratic matrix equation which can be defined be $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix; A,B and C are $n{\times}n$ given matrices with real elements. Newton's method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fr$\acute{e}$chet derivative is singular. Finally, we give some numerical examples.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.471-479
• /
• 2008

Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.

• Proceedings of the IEEK Conference
• /
• 1998.06a
• /
• pp.293-296
• /
• 1998

In this paper, we propose a matrix hypercube graph as a new topology for parallel computer and analyze its characteristics of the network parameters, such as degree, routing and diameter. N-dimensional matrix hypercube graph MH(2,n) contains 22n vertices and has relatively lower degree and smaller diameter than well-known hypercube graph. The matrix hypercube graph MH(2,n) and the hypercube graph Q2n have the same number of vertices. In terms of the network cost, defined as the product of the degree and diameter, the former has n2 while the latter has 4n2. In other words, it means that matrix hypercube graph MH(2,n) is better than hypercube graph Q2n with respect to the network cost.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.364-368
• /
• 1994

Algebraic matrix Riccati equations of the form, FP+PF$^{T}$ -PRP+Q=0. are analyzed with reference to the stability of closed-loop system F-PR. Here F, R and Q are n * n real matrices with R=R$^{T}$ and Q=Q$^{T}$ .geq.0 (nonnegative-definite). Such equations have been playing key roles in optimal control and filtering problems with R .geq. 0. and also in the solutions of in H$_{\infty}$ control problems with R taking the form R=H$_{1}$$^{T}$ H$_{1}$-H$_{2}$$^{T}$ H$_{2}$. In both cases an existence of stabilizing solution, i.e. the solution yielding asymptotically stable closed-loop system, is an important problem. First, we briefly review the typical results when R is of definite form, namely either R .geq. 0 as in LQG problems or R .leq. 0. They constitute two extrence cases of Riccati to the cases H$_{2}$=0 and H$_{1}$=0. Necessary and sufficient conditions are shown for the existence of nonnegative-definite or positive-definite stabilizing solution. Secondly, we focus our attention on more general case where R is only assumed to be symmetric, which obviously includes the case for H$_{\infty}$ control problems. Here, necessary conditions are established for the existence of nonnegative-definite or positive-definite stabilizing solutions. The results are established by employing consistently the so-called algebraic method based on an eigenvalue problem of a Hamiltonian matrix.x.ix.x.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.535-545
• /
• 2020

Let A be an m × n matrix over nonnegative integers. The isolation number of A is the maximum number of isolated entries in A. We investigate linear operators that preserve the isolation number of matrices over nonnegative integers. We obtain that T is a linear operator that strongly preserve isolation number k for 1 ≤ k ≤ min{m, n} if and only if T is a (P, Q)-operator, that is, for fixed permutation matrices P and Q, T(A) = P AQ or, m = n and T(A) = P A^tQ for any m × n matrix A, where A^t is the transpose of A.

• Journal of the Korean Statistical Society
• /
• v.7 no.2
• /
• pp.101-104
• /
• 1978

This paper considers the problem of estimating $\hat{\beta}$ in the case errors occur in observing the values of q-variables $X_1, X_2, ..., X_q$. The approximated estimator $\hat{\beta}(e)$ is obtained and its expected value, bias and covariance matrix are studied.