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Hwang, Suk-Geun Korean Mathematical Society 1989 대한수학회보 Vol.26 No.1
Let .ohm.$_{n}$ and Pm $t_{n}$ denote the sets of all n*n doubly stochastic matrices and the set of all n*n permutation matrices respectively. For m*n matrices A=[ $a_{ij}$ ], B=[ $b_{ij}$ ] we write A.leq.B(A<B) to mean that $a_{ij}$ .leq. $b_{ij}$ ( $a_{ij}$ < $b_{ij}$ ) for all i=1,..,m; j=1,..,n. Let $I_{n}$ denote the identity matrix of order n, let $J_{n}$ denote the n*n matrix all of whose entries are 1/n, and let $K_{n}$=n $J_{n}$. For a complex square matrix A, the permanent of A is denoted by per A. Let $E_{ij}$ denote the matrix of suitable size all of whose entries are zeros except for the (i,j)-entry which is one.hich is one.
Banach-Steinhaus theorem for a class of semi-continuous linear transformations
Hwang, Suk-geun 慶北大學校 師範大學 1980 敎育硏究誌 Vol.22 No.-
X를 Banach空間, Y를 norm을 갖는 線形空間이라 하자. 만약, X에서 Y에로의 半連續 線形變換의 한 class Γ가 空集合이 아니고, 또 각 x∈X에 對해 그의 orbit Γ(x)가 Y의 有界部分集合이라면 {||Λ|| : Λ∈Γ}는 有界인 實數의 集合이 된다. 즉 Γ는 X에서 Y로 가는 모든 有界線形變換 空間 R(X, Y)의 한 有界部分集合이 된다.
PERMUTATIONS WITH PARTIALLY FORBIDDEN POSITIONS
Hwang, Suk-Geun Korean Mathematical Society 2001 대한수학회지 Vol.38 No.4
In this paper we consider the enumeration problem of permutations with partially forbidden positions, generalizing the notion of permutations with forbidden positions. .As an alternative approach to this problem, we investigate the permanent maximization problem over some classes of (0,1)-matrices which have a given number of 1's some of which lie in prescribed positions.
The number of zeros of a tight sign-central matrix
Hwang, Suk-Geun,Kim, Ik-Pyo,Kim, Si-Ju,Lee, Sang-Gu Elsevier 2005 Linear algebra and its applications Vol.407 No.-
<P><B>Abstract</B></P><P>A real matrix <I>A</I> is called sign-central if A∼x=0 has a nonzero nonnegative solution <B>x</B> for every matrix A∼ with the same sign pattern as <I>A</I>. A sign-central matrix <I>A</I> is called tight sign-central if the Hadamard(entrywise) product of any two columns of <I>A</I> contains a negative component. Hwang et al. [S.G. Hwang, I.P. Kim, S.J. Kim, X.D. Zhang, Tight sign-central matrices, Linear Algebra Appl. 371 (2003) 225–240] proved that, for a positive integer <I>m</I>, there exists an <I>m</I>×<I>n</I> (0,1,−1) tight sign-central matrix <I>A</I> with no zero rows if and only if <I>m</I>+1⩽<I>n</I>⩽2<SUP><I>m</I></SUP>. They also determined the lower bound of the number of columns of a tight sign-central matrix with no zero rows in terms of the number of rows and the number of zero entries of the matrix along with the characterization of the equality case. For an <I>m</I>×<I>n</I> matrix <I>A</I>, the sparsity of <I>A</I> is the ratio <I>σ</I>(<I>A</I>)/<I>mn</I> where <I>σ</I>(<I>A</I>) denotes the number of zero entries of <I>A</I>.</P><P>In this paper, we determine the maximum number and the minimum number of zero entries of an <I>m</I>×<I>n</I> tight sign-central matrix with no zero rows for each pair (<I>m</I>,<I>n</I>) of positive integers with <I>m</I>+1⩽n⩽2<SUP><I>m</I></SUP>. We also determine the maximum sparsity of tight sign-central matrices with <I>m</I> nonzero rows in terms of <I>m</I> for each positive integer <I>m</I>.</P>
Spanning Column Ranks and Their Preservers of Nonnegative Matrices
Hwang, Suk-Geun,Song, Seok-Zun 濟州大學校 基礎科學硏究所 1997 基礎科學硏究 Vol.10 No.1
This paper concerns a certain column rank of matrices over the nonnegative reals; we call it the spanning column rank. We have a characterization of spanning column rand 1 matrices. We also investigate the linear operators which preserve the spanning column ranks of matrices over the nonnegative part of a certain unique factorization domain in the reals.