Related papers: Matrices similar to partial isometries

We classify the metric spaces that can be approximated by finite homogeneous ones.

We introduce a generalization of the b-metric we call a (b,c)-metric. We show that if $X$ is a $(b,c)$-metric space and $\psi: X \longrightarrow Y$ is a quasi-isometry then $Y$ is $(b,c)$-metrizable. We also define a particular kind of…

We show that almost commuting real orthogonal matrices are uniformly close to exactly commuting real orthogonal matrices. We prove the same for symplectic unitary matrices. This is in contrast to the general complex case, where not all…

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…

We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…

We give a canonical form of m-by-2-by-2 spatial matrices for equivalence over any field.

By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-P\'olya rearrangement inequality to positive definite matrices. The inequality is then extended to rectangular matrices. Using…

Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…

A partial Butson matrix is a matrix $H\in M_{M\times N}(\mathbb Z_q)$ having its rows pairwise orthogonal, where $\mathbb Z_q\subset\mathbb C^\times$ is the group of $q$-th roots of unity. We investigate here the counting problem for these…

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.

Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…

Let $A$ be an $n \times M$ matrix whose rows are orthonormal. Let $A_I$ be a submatrix of $A$ whose column indexes belong to the set $I$. Given $\epsilon >0$ we estimate the smallest cardinality of the set $I$, such that the operator $A_I$…

We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a…

Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process an equivalent to Witt's…

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than…

In this paper we study the semilinear partial differential equations in the plane the linear part of which is written in a divergence form. The main result is given as a factorization theorem. This theorem states that every weak solution of…

The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…

Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental…