Sparsity of orthogonal matrices with restrictions

✍ Scribed by Gi-Sang Cheon; Bryan L. Shader

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 99 KB
• Volume: 306
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00233-5

✦ Synopsis

The sparsity of orthogonal matrices which have k 1 columns of nonzeros is studied. It is shown that the minimum number of nonzero entries in such an m by m matrix is

As a consequence it is shown that if A is an m by n matrix with m < n and the properties that its rows are pairwise orthogonal, and it has less than

nonzero entries, then each vector orthogonal to the rows of A has at least one entry equal to 0. Also, for integers k and n with k n, the minimum number of nonzero entries in an n by n, connected, orthogonal matrix having a column with at least k nonzero entries is determined.