We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As an applica...
Tags: python, matrix, maya | Score: 1
Tags: r, dataframe, matrix, data-wrangling | Score: 0
This paper is concerned with the determination of a close real banded positive definite Toeplitz matrix in the Frobenius norm to a given square real banded matrix. While it is straightforward to determine the closest banded Toeplitz matrix to a given...
This study was aimed at simultaneously achieving sufficient accuracy and high performance for general matrix multiplications. Recent architectures, such as NVIDIA GPUs, feature high-performance units designed for low-precision matrix multiplications...
In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for multivariate analysis of variance (MANOVA) is discussed. The key to developing the distribution theory of eigenvalues of a singular random matrix is to us...
Consider a stochastic matrix $P$ and diagonal matrix $D.$ In this work, we introduce Tilted matrices. A Tilted matrix is the product $D'PD$, where $D'$ is a diagonal normalization that makes the product stochastic. We then provide several results on...
Using spectral factorization techniques, a method is given by which rational matrix solutions to the Leech equation with rational matrix data can be computed explicitly. This method is based on an approach by J.A. Ball and T.T. Trent, and generalizes...
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and then optim...
We identify the set of extreme points and apply Choquet theory to a normalized matrix-measure ball subject to finitely many linear side constraints. As an application we obtain integral representation formulas for the Herglotz class of matrix-valued...
We describe a new algorithm called Frequent Directions for deterministic matrix sketching in the row-updates model. The algorithm is presented an arbitrary input matrix $A \in R^{n \times d}$ one row at a time. It performed $O(d \times \ell)$ operati...
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as well as pos...
We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix. Specifically, the ideals we consider are generated...
We consider the problem of placing $n$ nonattacking queens on a symmetric $n \times n$ Toeplitz matrix. As in the $N$-queens Problem on a chessboard, two queens may attack each other if they share a row or a column in the matrix. However, the usual d...
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle matrix-vector mul...
We study level statistics in ensembles of integrable $N\times N$ matrices linear in a real parameter $x$. The matrix $H(x)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i(x)$ (integrals of...
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of inte...
These results are a contribution to the model theory of matrix consequence. We give a semantic characterization of uniform and couniform consequence relations. These properties have never been treated individually, at least in a semantic manner. We c...
This **Part 2, The Matrix** is a continuation of [**Part 1, Finkle Is Einhorn**](https://www.reddit.com/r/Superstonk/comments/owpfc3/will_the_real_gme_bbemg_please_stand_up_part_1/). A revision of Par...