Related papers: On a determinantal inequality arising from diffusi…

We consider a square random matrix of size N of the form A + Y where A is deterministic and Y has iid entries with variance 1/N. Under mild assumptions, as N grows, the empirical distribution of the eigenvalues of A+Y converges weakly to a…

We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble…

We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful…

Let $A$, $B$ be multidimensional matrices of boundary format respectively $\prod_{i=0}^p(k_i+1)$, $\prod_{j=0}^q(l_j+1)$. Assume that $k_p=l_0$ so that the convolution $A\ast B$ is defined. We prove that $Det (A\ast B)=Det(A)^{\alpha}\cdot…

We relate Nekrasov partition functions, with arbitrary values of $\epsilon_1,\epsilon_2$ parameters, to matrix models for $\beta$-ensembles. We find matrix models encoding the instanton part of Nekrasov partition functions, whose measure,…

Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness of linear series of the form dH - E on…

Several new improvements of the $A$-numerical radius inequalities for operators acting on a semi-Hilbert space, i.e., a space generated by a positive operator $A$, are proved. In particular, among other inequalities, we show that…

We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…

In this paper, we present a new formula of the determinant tensor $det_n$ for $n \times n$ matrices. In \cite{kim2023newdet4}, Kim, Ju, and Kim found a new formula of $4 \times 4$ determinant tensor $det_4$ which is available when the base…

We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…

4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It…

Under binary matrices we mean matrices whose entries take one of two values. In this paper, explicit formulae for calculating the determinant of some type of binary Toeplitz matrices are obtained. Examples of the application of the…

Given a matrix $A$, let $A_{I,J}$ denote the submatrix of $A$ determined by rows $I$ and columns $J$. Fischer's Inequalities state that for each $n \times n$ Hermitian positive semidefinite matrix $A$, and each subset $I$ of…

We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…

The objective of this note is to establish the Determinant Majorization Formula $F(A)^{1\over N} \geq \det(A)^{1\over n}$ for all operators $F$ determined by an invariant Garding-Dirichlet polynomial of degree $N$ on symmetric $n \times n$…

Given two positive definite matrices $A$ and $B$, a well known result by Gelfand, Naimark and Lidskii establishes a relationship between the eigenvalues of $A$ and $B$ and those of $AB$ by means of majorization inequalities. In this work we…

In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].

Given a set of inequalities determined by homogeneous forms, the following intertwined results are established: (1) the volume of the real semi-algebraic domain determined by these inequalities is explicitly determined; it is shown to be…

Let $G = (G,+)$ be a compact connected abelian group, and let $\mu_G$ denote its probability Haar measure. A theorem of Kneser (generalising previous results of Macbeath and Raikov) establishes the bound $$ \mu_G(A + B) \geq \min(…

The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…