相关论文: Compounding Doubly Affine Matrices
We consider products of independent random matrices taken from the induced Ginibre ensemble with complex or quaternion elements. The joint densities for the complex eigenvalues of the product matrix can be written down exactly for a product…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
An $n\times n$ symmetric matrix $A$ is copositive if the quadratic form $x^TAx$ is nonnegative on the nonnegative orthant $\mathbb{R}^{n}_{\geq 0}$. The cone of copositive matrices contains the cone of matrices which are the sum of a…
We construct and classify all possible Magic Squares (MS's) related to Euclidean or Lorentzian rank-3 simple Jordan algebras, both on normed division algebras and split composition algebras. Besides the known Freudenthal-Rozenfeld-Tits MS,…
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for…
In this rather brief note we present and discuss techniques for solving Kronecker matrix product least squares problems. Our main contribution is an iterative approach that uses the efficient Kronecker matrix-vector multiplication strategy…
Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first…
A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…
We propose a simple algorithm for generating Binary Magic Squares (BMS), i.e., square binary matrices where the sum of all rows and all columns are equal. We show by induction that our algorithm always returns valid BMS with optimal…
The canonical polyadic decomposition (CPD) is a compact decomposition which expresses a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is computing a generalized eigenvalue decomposition (GEVD) of the…
We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such representations is of the expected order of magnitude. We…
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…
An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends…
The combined matrix is a very useful concept for many applications. Almost strictly sign regular (ASSR) matrices form an important structured class of matrices with two possible zero patterns, which are either type-I staircase or type-II…
The set of sums of two squares plays a significant role in elementary number theory. In this article, we establish the existence of several rich monochromatic configurations in the natural numbers by exploiting algebraic structures induced…
Algebraic Combinatorics originated in Algebra and Representation Theory, studying their discrete objects and integral quantities via combinatorial methods which have since developed independent and self-contained lives and brought us some…
We consider the problem of recovering a unitary eigendecomposition of a complex unitary matrix from that of its embedded real-valued formulation. Such formulations arise naturally in scientific computing workflows that employ…
We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module $A$ has order $p$ or $2p$,…
Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…
A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation…