We study the recovery of Hermitian low rank matrices X ∈ Cn×n from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form ajaj for some measurement vectors a1, . . . , am, i.e., the measurements are given by yj = tr(Xaja ∗ j ). The case where the matrix X = xx ∗ to...

Motivated by the sequence form formulation of Koller et al. [19], this paper defines bilinear games, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games with compact polytopal strategy sets and two payoff matrices (A, B) such that when (x, y) is the played strategy profile, the payoffs of the players are xTAy and xTBy ...

For a prime p, we consider some natural classes of matrices over a finite field Fp of p elements, such as matrices of given rank or with characteristic polynomial having irreducible divisors of prescribed degrees. We demonstrate two different techniques which allow us to show that the number of such matrices in each of these classes and also with components in a given subinterval [−H,H] ⊆ [−(p ...

For nonsingular n× n (n ≥ 6) pentadiagonal matrices P having nonzero entries on its second subdiagonal, we propose a procedure for computing both the determinant detP in O(n) times, and accurate information for obtaining the inverse P−1 in O(n) times. In the general nonsingular case, n ≥ 5, a suitable decomposition of P, as a product of two nonsingular upper Hessenberg matrices, allows us anoth...

We investigate the problem of completing partial matrices to rank-1 probability matrices. The motivation for studying this problem comes from statistics: A lack of desired completion can provide a falsification test for partial observations to come from the independence model. For each type of partial matrix, we give an inequality in the observed entries which is satisfied if and only if a desi...