Related papers: Simultaneous unitary equivalences
We present a necessary and sufficient condition for a 3 by 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test generalizes to a…
Two matrices $A$ and $B$ are called unitary (resp. orthogonal) equivalent if $AU=VB$ for two unitary (resp. orthogonal) matrices $U$ and $V$. Using trace identities, criteria are given for simultaneous unitary, orthogonal or complex…
We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…
We present an algorithm to solve the Simultaneous Unitary Similarity(S.U.S) problem which is to check if there exists a Similarity transformation determined by a Unitary $U$ s.t $UA_lU^*=B_l$, $l \in \{1,...,p\}$, where $A_l$ and $B_l$ are…
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
Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i) are not similar to direct sums of matrices of smaller…
We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix.…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
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…
It is known that if A and B are two n-by-n complex matrices and (A,A^T) is simultaneously equivalent to (B,B^T), then A is congruent to B. We extend this statement to multilinear forms.
We construct six unitary trace invariants for 2 by 2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We prove two quaternionic versions of a well known…
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…
Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
We give an universal algorithm for testing the local unitary equivalence of states for multipartite system with arbitrary dimensions.
Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only…
Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…
A simple recursive scheme for parameterisation of n-by-n unitary matrices is presented.