• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제24권1호
• /
• pp.85-91
• /
• 2020

In this parer we express the sufficient conditions under which it is proved that a J-normal irreduciable Hessenberg matrix is tridiagonal and it is also proved that a similar statement exists for J-conjugate normal matrices

• 대한수학회지
• /
• 제43권1호
• /
• pp.215-224
• /
• 2006

We call the bipartite graph G is normal provided the reduced adjacency matrix A of G is normal. In this paper we give graph representations of normal matrices. In addition we shall have the characterization of signed bipartite normal graphs.

• 충청수학회지
• /
• 제16권1호
• /
• pp.25-36
• /
• 2003

We study the question of whether a partial (0, 1)-normal matrix has a non-symmetric normal completion. Matrix sandwich problems are an important and special case of matrix completion problems. In this paper, we give some properties for the (0, 1)-normal matrices and some large classes that satisfies the normal sandwich completion.

• Communications for Statistical Applications and Methods
• /
• 제7권1호
• /
• pp.285-290
• /
• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• Journal of applied mathematics & informatics
• /
• 제29권3_4호
• /
• pp.641-651
• /
• 2011

In this paper, with use of the displacement matrix, two special matrices are constructed. By these special matrices the block decompositions of the block symmetric Hankel matrix and the inverse of the Hankel matrix are derived. Hence, the algorithms according to these decompositions are given. Furthermore, the numerical tests show that the algorithms are feasible.

• Journal of applied mathematics & informatics
• /
• 제31권3_4호
• /
• pp.545-558
• /
• 2013

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

• Communications for Statistical Applications and Methods
• /
• 제7권1호
• /
• pp.55-64
• /
• 2000

We propose a criterion for testing homogeneity of matrix intraclass covariance matrices of K multivariate normal populations, It is based on a variable transformation intended to propose and develop a likelihood ratio criterion that makes use of properties of eigen structures of the matrix intraclass covariance matrices. The criterion then leads to a simple test that uses an asymptotic distribution obtained from Box's (1949) theorem for the general asymptotic expansion of random variables.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제23권3호
• /
• pp.267-282
• /
• 2019

This paper examines how one can build a block tridiagonal structure for k-almost normal matrices and also for k-almost conjugate normal matrices. We shall see that these representations are created by unitary similarity and unitary congruance transformations, respectively. It shall be proven that the orders of diagonal blocks are 1, k + 2, 2k + 3, ${\ldots}$, in both cases. Then these block tridiagonal structures shall be reviewed for the cases where the mentioned matrices satisfy in a second-degree polynomial. Finally, for these processes, algorithms are presented.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1061-1071
• /
• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1429-1433
• /
• 2009

The likelihood distance for the joint distribution of two multivariate normal distributions with common covariance matrix is explicitly derived. It is useful for identifying outliers which do not follow the joint multivariate normal distribution with common covariance matrix. The likelihood distance derived here is a good ground for the use of a generalized Wilks statistic in influence analysis of two multivariate normal data.