• Honam Mathematical Journal
• /
• v.26 no.1
• /
• pp.3-15
• /
• 2004

In the fuzzy theory, a matrix A is idempotent if $A^2=A$. The idempotent fuzzy matrices are important in various applications and have many interesting properties. Using the upper diagonal completion process, we have the zero patterns of idempotent fuzzy matrix, that is, the idempotent Boolean matrices. In addition, we give the construction of all idempotent fuzzy matrices for each dimension n.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2002.03a
• /
• pp.475-482
• /
• 2002

This paper provides the systematic procedure to determine the weighting matrices of optimal controllers considering structural energy. Optimal controllers consist of LQR and ILQR. The weighting matrices are needed first in the conventional optimal control design strategy. However, they are in general dependent on the experienced knowledge of controll designers. Applying the Lyapunov function to the total structural energy and using the contrition that its derivative is negative, we can determine the weighting matrices without difficulty. It is proven that the control efficiency is achieved well for LQR and ILQR.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.651-658
• /
• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• Korean Journal of Mathematics
• /
• v.26 no.3
• /
• pp.349-371
• /
• 2018

Some inequalities for quantum f-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and ${\chi}^2-distance$ are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.119-129
• /
• 1999

In [1], it was shown that for $n\geq 2$ the least number of nonzero entries in an $n\times n$ orthogonal matrix is not direct summable is 4n-4, and zero patterns of the $n\times n$ orthogonal matrices with exactly 4n-4 nonzero entries were determined. In this paper, we construct $n\times n$ orthogonal matrices with exactly 4n-r nonzero entries. furthermore, we determine m${\times}$n sparse row-orthogonal matrices.

• Proceedings of the KIEE Conference
• /
• 2004.07e
• /
• pp.45-48
• /
• 2004

This paper presents a new method for finding the Block Pulse series coefficients, deriving the Block Pulse integration operational matrices and generalizing the integration operational matrices which are necessary for the control fields using the Block Pulse functions. In order to apply the Block Pulse function technique to the problems of state estimation or parameter identification more efficiently. it is necessary to find the more exact value of the Block Pulse series coefficients and integral operational matrices.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.475-484
• /
• 2004

In general, a matrix A is idempotent if $A^2$ = A. The idempotent matrices play an important role in the matrix theory and some properties of the Boolean matrices are examined. Using the upper diagonal completion process, we give the characterization of the Boolean idempotent matrices in modified Frobenius normal form.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.91-107
• /
• 2004

The fuzzy matrices are successfully used when fuzzy uncertainty occurs in a problem. Fuzzy matrices become popular for last two decades. In this paper, two new binary fuzzy operators (equation omitted) and (equation omitted) are introduced for fuzzy matrices. Several properties on (equation omitted) and (equation omitted) are presented here. Also, some results on existing operators along with these new operators are presented.

• Journal of the Korean Mathematical Society
• /
• v.36 no.5
• /
• pp.1009-1020
• /
• 1999

The minimum permanent and the set of minimizing matrices over the face of the polytope n of all doubly stochastic matrices of order n determined by any staircase matrix was determined in [4] in terms of some parameter called frame. A staircase matrix can be described very simply as a Ferrers matrix by its row sum vector. In this paper, some simple exposition of the permanent minimization problem over the faces determined by Ferrers matrices of the polytope of n are presented in terms of row sum vectors along with simple proofs.

• Journal of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.469-487
• /
• 1999

Sign patterns of idempotent matrices, especially symmetric idempotent matrices, are investigated. A number of fundamental results are given and various constructions are presented. The sign patterns of symmetric idempotent matrices through order 5 are determined. Some open questions are also given.