Balanced matrices

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Balanced matrices

"Dipartimento di Matematica Pura ed Applicata, Universiti di Padova, Via Belzoni 7, 35131 Padova, Italy. tCarnegie Mellon University, Schenley Park, Pittsburgh, PA 15213. ICarnegie Mellon University, Schenley Park, Pittsburgh, PA 15213. §Indian Institute of Management, Bannerghatta rd. 560076 Bangalore, India. 1 Carnegie Mellon University, Schenley Park, Pittsburgh, PA 15213. This work was supp...

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Decomposition of Balanced Matrices

A 0; 1 matrix is balanced if it does not contain a square submatrix of odd order with two ones per row and per column. We show that a balanced 0,1 matrix is either totally unimodular or its bipartite representation has a cutset consisting of two adjacent nodes and some of their neighbors. This result yields a polytime recognition algorithm for balancedness. To prove the result, we rst prove a d...

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Hsiao-Code Check Matrices and Recursively Balanced Matrices

The key step of generating the well-known Hsiao code is to construct a {0, 1}-check-matrix in which each column contains the same odd-number of 1’s and each row contains the same number of 1’s or differs at most by one for the number of 1’s. We also require that no two columns are identical in the matrix. The author solved this problem in 1986 by introducing a type of recursively balanced matri...

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Balanced 0-1 Matrices I. Decomposition

A 0, \1 matrix is balanced if, in every square submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This paper extends the decomposition of balanced 0, 1 matrices obtained by Conforti, Cornue jols, and Rao (1999, J. Combin. Theory Ser. B 77, 292 406) to the class of balanced 0, \1 matrices. As a consequence, we obtain a polynomial time algorithm f...

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Extremal Properties of Balanced Tri-Diagonal Matrices

If A is a square matrix with distinct eigenvalues and D a nonsingular matrix, then the angles between rowand column-eigenvectors of D~XAD differ from the corresponding quantities of A. Perturbation analysis of the eigenvalue problem motivates the minimization of functions of these angles over the set of diagonal similarity transforms ; two such functions which are of particular interest are the...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2006

ISSN: 0012-365X

DOI: 10.1016/j.disc.2005.12.033