Invertibility of 2 × 2 operator matrices

Further inequalities for operator space numerical radius on 2*2 operator ‎matrices

‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

A NOTE VIA DIAGONALITY OF THE 2 × 2 BHATTACHARYYA MATRICES

In this paper, we consider characterizations based on the Bhattacharyya matrices. We characterize, under certain constraint, dis tributions such as normal, compound poisson and gamma via the diago nality of the 2 X 2 Bhattacharyya matrix.

Invertibility of symmetric random matrices

We study n × n symmetric random matrices H, possibly discrete, with iid abovediagonal entries. We show that H is singular with probability at most exp(−nc), and ‖H−1‖ = O(√n). Furthermore, the spectrum of H is delocalized on the optimal scale o(n−1/2). These results improve upon a polynomial singularity bound due to Costello, Tao and Vu, and they generalize, up to constant factors, results of T...

Invertibility of Matrices of Field Elements

In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of fiel...

Invertibility of Random Matrices Lecture Notes