Related papers: Characterization of half-radial matrices

The $1/x^{2}$ deformed $c=1$ matrix model is studied at finite radius and non-zero cosmological constant. Calculational techniques are presented and illustrated in some examples. Furthermore, a new kind of $R \rightarrow 1/R$ duality is…

Let $A=\begin{bmatrix} A_{ij} \end{bmatrix}$ be an $n\times n$ operator matrix, where each $A_{ij}$ is a bounded linear operator on a complex Hilbert space. Among other numerical radius bounds, we show that $w(A)\leq w(\hat{A})$, where…

The matricial range of the $2\times2$ matrix $E_{21}$ (i.e., the $2\times 2$ unilateral shift) is described very simply: it consists of all matrices with numerical radius at most $1/2$. The known proofs of this simple statement, however,…

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…

We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices…

An $r$-graph is an $r$-regular graph with no odd cut of size less than $r$. A well-celebrated result due to Lov\'asz says that for such graphs the linear system $Ax = \textbf{1}$ has a solution in $\mathbb{Z}/2$, where $A$ is the $0,1$ edge…

Several upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices are developed which refine and generalize the earlier related bounds. In particular, we show that if $B,C$ are bounded linear operators on a complex…

The celebrated Dvoretzky theorem asserts that every $N$-dimensional convex body admits central sections of dimension $d = \Omega(\log N)$, which is nearly spherical. For many instances of convex bodies, typically unit balls with respect to…

Given a graph $G$, the unraveled ball of radius $r$ centered at a vertex $v$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We prove a lower bound on the maximum spectral radius of unraveled balls of fixed radius,…

In this paper, we introduce the notion of almost Armendariz ring which is the generalization of Armendariz ring and discuss some of its properties. We prove that a ring R is almost Armendariz if and only if n X n upper triangular matrix…

For $n$-by-$n$ and $m$-by-$m$ complex matrices $A$ and $B$, it is known that the inequality $w(A\otimes B)\le\|A\|w(B)$ holds, where $w(\cdot)$ and $\|\cdot\|$ denote, respectively, the numerical radius and the operator norm of a matrix. In…

Let A be a matrix whose entries are real i.i.d. centered random variables with unit variance and suitable moment assumptions. Then the smallest singular value of A is of order n^{-1/2} with high probability. The lower estimate of this type…

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matriz is superregular if all of its minors that are not trivially zero are nonzero. Given a a times b, a larger than or equal to b,…

We define the complete numerical radius norm for homomorphisms from any operator algebra into ${\mathcal B}({\mathcal H})$, and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show…

For any $n$-by-$n$ matrix $A$ of the form \[[\begin{array}{cccc} 0 & A_1 & & \\ & 0 & \ddots & \\ & & \ddots & A_{k-1} \\ & & & 0\end{array}],\] we consider two $k$-by-$k$ matrices \[A'=[\begin{array}{cccc} 0 & \|A_1\| & & \\ & 0 & \ddots &…

We characterize the infimum of a matrix norm of a square matrix A induced by an absolute norm, over the fields of real and complex numbers. Usually this infimum is greater than the spectral radius of A. If A is sign equivalent to a…

Let $A$ be an element of the copositive cone ${\cal C}_n$. A zero $u$ of $A$ is a nonzero nonnegative vector such that $u^TAu = 0$. The support of $u$ is the index set $\mbox{supp}u \subset \{1,\dots,n\}$ corresponding to the positive…

In this paper, we introduce a notion of the center and radius of a subset A of metric space X. In the Euclidean spaces, this notion can be seen as the extension of the center and radius of open/closed balls. The center and radius of a…

Let $a$ be a positive element in a unital $C^*$-algebra $\mathfrak{A}$. We define a semi-norm on $\mathfrak{A}$, which generalizes the $a$-operator semi-norm and the $a$-numerical radius. We investigate basic properties of this semi-norm…

Using the polar decomposition of a bounded linear operator $A$ defined on a complex Hilbert space, we obtain several numerical radius inequalities of the operator $A$, which generalize and improve the earlier related ones. Among other…