Almost orthogonal submatrices of an orthogonal matrix

Almost Orthogonal Submatrices of an Orthogonal Matrix

Let t ≥ 1 and let n, M be natural numbers, n < M. Let A = (a i,j) be an n × M matrix whose rows are orthonormal. Suppose that for all j M n · n i=1 a 2 i,j 1/2 ≤ t.

On Almost Orthogonal Frames

On the Nonsingularity of Principal Submatrices of a Random Orthogonal Matrix

Let S be a random nonnegative definite matrix and let G be an orthogonal matrix such that S = GDG', where D is the diagonal matrix of the latent roots of S. In this note, we prove _ r G t t Gt21 the a.s. existence of G~I, where G-tc2~ c=j, under some weak conditions on the distribution of S. AMS Subject Classification: Primary 62H10, 60D05.

Complex Orthogonal Designs with Forbidden 2 × 2 Submatrices

Complex orthogonal designs (CODs) are used to construct space-time block codes. COD Oz with parameter [p, n, k] is a p × n matrix, where nonzero entries are filled by ±zi or ±z ∗ i , i = 1, 2, . . . , k, such that O H z Oz = (|z1| 2 + |z2| 2 + . . . + |zk| )In×n. Define Oz an M-type COD if and only if Oz does not contain submatrix (

Complex Orthogonal Designs with Forbidden $2 \times 2$ Submatrices

Complex orthogonal designs (CODs) are used to construct space-time block codes. COD Oz with parameter [p, n, k] is a p × n matrix, where nonzero entries are filled by ±zi or ±z ∗ i , i = 1, 2, . . . , k, such that O H z Oz = (|z1| 2 + |z2| 2 + . . . + |zk| )In×n. Define Oz a first type COD if and only if Oz does not contain submatrix (