Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CONSTRUCTIONS FOR THE SPARSEST ORTHOGONAL MATRICES

  • Cheon, Gi-Sang (Department of Mathematics, Daejin University) ;
  • Shader, Bryan L. (Department of Mathematics, University of Wyoming)
  • Published : 1999.02.01
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Abstract

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.

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References

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  2. J. of Combinatorial Theory Series A v.85 How sparse can a matrix with orthogonal rows be? G.-S. Cheon;B. L. Shader
  3. Discrete Applied Mathematics J. Sparse orthogonal matrices and the Haar wavelet G.-S. Cheon;B. L. Shader
  4. Matrix computations(3rd, ed.) G. H. Golub;C. F. V. Loan
  5. Rocky Mtn. Math. J. A simple proof of Fiedler's conjecture concerning orthogonal matrices B. L. Shader