Related papers: Birational equivalence of exponential matrices

Let $\Bigl\langle\matrix{n\cr k}\Bigr\rangle$, $\Bigl\langle\matrix{B_n\cr k}\Bigr\rangle$, and $\Bigl\langle\matrix{D_n\cr k}\Bigr\rangle$ be the Eulerian numbers in the types A, B, and D, respectively -- that is, the number of…

Let $X$ be a projective variety of dimension $r$ over an algebraically closed field. It is proven that two birational embeddings of $X$ in $\P^n$, with $n\geq r+2$ are equivalent up to Cremona transformations of $\P^n$.

In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions…

For two matrices $A$ and $B$, and large $n$, we show that most products of $n$ factors of $e^{A/n}$ and $n$ factors of $e^{B/n}$ are close to $e^{A + B}$. This extends the Lie-Trotter formula. The elementary proof is based on the relation…

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…

In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

This work is about symbolic powers of codimension two perfect ideals in a standard polynomial ring over a field, where the entries of the corresponding presentation matrix are general linear forms. The main contribution of the present…

We present necessary and sufficient conditions for an n\times n complex matrix B to be unitarily similar to a fixed unicellular (i.e., indecomposable by similarity) n\times n complex matrix A

We study the combinatorial properties of final types, which are certain non-decreasing sequences of integers, together with the partitions naturally associated with them. As a consequence, we obtain an identity expressing the $n$-nacci…

In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…

If L, respectively R are matrices with entries binom{i-1,j-1}, respectively binom{i-1,n-j}, it is known that L^2 = I (mod 2), respectively R^3 = I (mod 2), where I is the identity matrix of dimension n > 1 (see P10735-May 1999 issue of the…

In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider…

There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative case is that our noncommutative exponentials can be defined…

We obtain an iterative formula that converges incrementally to the smallest singular value. Similarly, we obtain an iterative formula that converges decreasingly to the largest singular value.

Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a class of indecomposable positive maps in the algebra of 2n x 2n complex matrices with n>1. It is shown that these maps are exposed and hence…

In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…

We propose a specific class of matrices which participate in factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang-Baxter maps, expressed in non-commutative variables.…