相关论文: A Canonical Representation of Block Matrices with …
We introduce Block Sparse Canonical Correlation Analysis which estimates multiple pairs of canonical directions (together a "block") at once, resulting in significantly improved orthogonality of the sparse directions which, we demonstrate,…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
The Kalman canonical form for quantum linear systems was derived in \cite{ZGPG18}. The purpose of this paper is to present an alternative derivation by means of a Gramian matrix approach. Controllability and observability Gramian matrices…
In this work, new closed-form formulas for the matrix exponential are provided. Our method is direct and elementary, it gives tractable and manageable formulas not current in the extensive literature on this essential subject. Moreover,…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
We give an explanation of the $\mathrm{d}\log$-form of the coefficient matrix of canonical differential equations using the projection of ($n$+1)-$\mathrm{d}\log$ forms onto $n$-$\mathrm{d}\log$ forms. This projection is done using the…
In this paper, we aim to estimate block-diagonal covariance matrices for Gaussian data in high dimension and in fixed dimension. We first estimate the block-diagonal structure of the covariance matrix by theoretical and practical estimators…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…
Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
Using the decomposition of semimagic squares into the associated and balanced symmetry types as a motivation, we introduce an equivalent representation in terms of block-structured matrices. This block representation provides a way of…
We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input…
Calculating the log-determinant of a matrix is useful for statistical computations used in machine learning, such as generative learning which uses the log-determinant of the covariance matrix to calculate the log-likelihood of model…
Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields.…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
We examine some properties of the non-normalized (or canonical) density matrix in the coherent states representation, by two equivalent ways. On the one hand by its definition, and on the other hand as a solution to Bloch's canonical…