The possible numbers of zeros in an orthogonal matrix. (English) Zbl 0918.15007

Cheon, G.-S.; Johnson, C. R.; Lee, S.-G.; Pribble, E. J.

Electron. J. Linear Algebra 5, 19-23 (1999).

It is shown that for \(n\geq 2\) there is an \(n\times n\) indecomposable orthogonal matrix with exactly \(k\) entries equal to zero if and only if \(0\leq k\leq (n-2)^2\).

Reviewer: G.Bonanno (Davis)

MSC:

15B57	Hermitian, skew-Hermitian, and related matrices
05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)

Keywords:

numbers of zeros; indecomposable matrix; orthogonal matrix