• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.333-344
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• 1999

In [4], it was shown that an n by n orthogonal matrix which has a row of nonzeros has at least ( log2n + 3)n - log2n +1 nonzero entries. In this paper, the matrices achieving these bounds are constructed. The analogous sparsity problem for m by n row-orthogonal matrices which have a row of nonzeros in conjectured.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.233-244
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• 2004

The influence of observations is investigated in fitting proportional covariance matrices model. Local influence measures are obtained when all parameters or subsets of the parameters are of interest. We will also derive the local influence measure for investigating the influence of observations in testing the proportionality of covariance matrices. A numerical example is given for illustration.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.849-856
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• 1995

There are some papers on structure theorems for the spaces of matrices over certain semirings. Beasley, Gregory and Pullman [1] obtained characterizations of semiring rank 1 matrices over certain semirings of the nonnegative reals. Beasley and Pullman [2] also obtained the structure theorems of Boolean rank 1 spaces. Since the semiring rank of a matrix differs from the column rank of it in general, we consider a structure theorem for semiring rank in [1] in view of column rank.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.841-849
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• 1997

A square matrix A with $per A \neq 0$ is called convertible if there exists a {1, -1} matrix H such that $per A = det(H \circ A)$ where $H \circ A$ denote the Hadamard product of H and A. In this paper, ranks of convertible {0, 1} matrices are investigated and the existence of maximal convertible matrices with its rank r for each integer r with $\left\lceil \frac{n}{2} \right\rceil \leq r \leq n$ is proved.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.943-950
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• 2003

The maximal column rank of an m by n matrix A over max algebra is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over max algebra. We also characterize the linear operators which preserve the maximal column rank of matrices over max algebra.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.695-704
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• 2018

In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.73-88
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• 2016

We consider ${\mathcal{T}}_{\infty}(F)$ - the space of all innite upper triangular matrices over a eld F. We give a description of all linear maps that satisfy the property: if rank(x) = 1, then $rank({\phi}(x))=1$ for all $x{\in}{\mathcal{T}}_{\infty}(F)$. Moreover, we characterize all injective linear maps on ${\mathcal{T}}_{\infty}(F)$ such that if rank(x) = k, then $rank({\phi}(x))=k$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.373-385
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• 2009

An m${\times}$n Boolean matrix A is called regular if there exists an n${\times}$m Boolean matrix X such that AXA = A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1421-1441
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• 2017

We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.201-209
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• 2004

We define the incidence matrices of oriented and nonoriented ${\kappa}$-hypergraphs, respectively. We discuss the ranks of some circulant matrices and show that the rank of the incidence matrices of oriented and nonoriented ${\kappa}$-hypergraphs H are $n$ under a certain condition on the ${\kappa}$-edge set or ${\kappa}$-arc set of H.