Constructions for the sparsest orthogonal matrices
Bull. Korean Math. Soc. 1999 Vol. 36, No. 1, 119-129
Gi-Sang Cheon and Bryan L. Shader
Daejin University, University of Wyoming
Abstract : In [1], it was shown that for $n\ge2$ the least number of nonzero entries in an $n\times n$ orthogonal matrix which 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 $4n-4$ nonzero entries. Furthermore, we determine $m\times n$ sparse row-orthogonal matrices.
Keywords : sparse orthogonal matrix, basic orthogonal matrix
MSC numbers : Primary 05A15, Secondary 65F25
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