• Honam Mathematical Journal
• /
• v.19 no.1
• /
• pp.157-164
• /
• 1997

We are concerned with three classes of matrices that are relevant to the linear complementary problem. We prove that within the class of $P_0$-matrices, the Q-matrices are precisely the regular matrices and we show that the same characterizations hold for an L-matrix as well, and that the symmetric copositive-plus Q-matrices are precisely those which are strictly copositive.

• Kyungpook Mathematical Journal
• /
• v.46 no.1
• /
• pp.89-96
• /
• 2006

For a rank-1 matrix A, there is a factorization as $A=ab^t$, the product of two vectors a and b. We characterize the linear operators that preserve rank and some equivalent condition of rank-1 matrices over a chain semiring. We also obtain a linear operator T preserves the rank of rank-1 matrices if and only if it is a form (P, Q, B)-operator with appropriate permutation matrices P and Q, and a matrix B with all nonzero entries.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.45 no.7
• /
• pp.17-21
• /
• 2008

As with the binary pseudo-random sequences q-ary m-sequences possess very good properties which make them useful in many applications. So we construct a class of Jacket matrices by applying additive characters of the finite field $F_q$ to entries of all shifts of q-ary m-sequence. In this paper, we generalize a method of obtaining conventional Hadamard matrices from binary PN-sequences. By this way we propose Jacket matrix construction based on q-ary M-sequences.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.659-670
• /
• 2008

We denote by $\mathcal{Q}$(A) the set of all real matrices with the same sign pattern as a real matrix A. A matrix A is an SN-matrix provided there exists a set S of sign pattern such that the set of sign patterns of vectors in the -space of $\tilde{A}$ is S, for each ${\tilde{A}}{\in}\mathcal{Q}(A)$. Some properties of SN-matrices arc investigated.

• Honam Mathematical Journal
• /
• v.26 no.3
• /
• pp.341-353
• /
• 2004

We denote by ${{\mathcal{Q}}(A)}$ the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set ${\mathcal{S}}$ of sign patterns such that the set of sign patterns of vectors in the null-space of ${\tilde{A}}$ is ${\mathcal{S}}$, for each ${\tilde{A}}{\in}{{\mathcal{Q}}(A)}$. Some properties of matrices with signed null-spaces are investigated.

• 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.

• Honam Mathematical Journal
• /
• v.42 no.2
• /
• pp.235-249
• /
• 2020

Let Q and R be the well-known matrices associated with Fibonacci and Lucas numbers, and k, m, and n be any integers. It is mainly established all solutions of the matrix equations c₁Qⁿ + c₂Q^m = Q^k, c₁Qⁿ + c₂Q^m = RQ^k, and c₁Qⁿ + c₂RQ^m = Q^k with unknowns c₁, c₂ ∈ ℂ*. Moreover, using the obtained results, it is presented many identities, some of them are available in the literature, and the others are new, related to the Fibonacci and Lucas numbers.

• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.343-352
• /
• 2013

In this paper, we give a formula of $(P+Q)^D$ under the conditions $P^2Q+QPQ=0$ and $P^3Q=0$. Then applying it to give some results of block matrix $M=(^A_C^B_D)$ (A and D are square matrices) with generalized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.643-652
• /
• 2008

We construct the sets of Boolean matrix pairs, which are naturally occurred at the extreme cases for the Boolean rank inequalities relative to the sums and difference of two Boolean matrices or compared between their Boolean ranks and their real ranks. For these sets, we consider the linear operators that preserve them. We characterize those linear operators as T(X) = PXQ or $T(X)\;=\;PX^tQ$ with appropriate invertible Boolean matrices P and Q.

• Journal of applied mathematics & informatics
• /
• v.39 no.5_6
• /
• pp.703-715
• /
• 2021

There are several methods for constructing self-dual codes. Among them, the building-up construction is a powerful method. Recently, Kim and Choi proposed special building-up constructions which use symmetric generator matrices for self-dual codes over GF(q), where q is odd. In this paper, we study the same method when q is even.