Related papers: A Note on the Classification of Permutation Matrix

We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative…

This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…

The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…

Let $m, n$ be positive integers such that $m>1$ divides $n$. In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1, n]:=\{1, \ldots, n\}$ with the property that the reduction $\pmod m$ of $m$…

We prove that one can realize certain triangulated subcategories of the singularity category of a complete intersection as homotopy categories of matrix factorizations. Moreover, we prove that for any commutative ring and non-zerodivisor,…

We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

In this paper, some tensor commutation matrices are expressed in termes of the generalized Pauli matrices by tensor products of the Pauli matrices.

This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…

This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…

Racks and quandles are rich algebraic structures that are strong enough to classify knots. Here we develop several fundamental categorical aspects of the theories of racks and quandles and their relation to the theory of permutations. In…

Motivated by classification, up to order isomorphism, of some dense subgroups of Euclidean space that are free of minimal rank, we obtain apparently new invariants for an equivalence relation (intermediate between Hermite and Smith) on…

We first obtain the most general and compact parametrization of the unitary transformation diagonalizing any 3 by 3 hermitian matrix H, as a function of its elements and eigenvalues. We then study a special class of fermion mass matrices,…

For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…

Birkhoff polytope is the set of all bistochastic matrices (also known as doubly stochastic matrices). Bistochastic matrices form a special class of stochastic matrices where each row and column sums up to one. Permutation matrices and…

In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…

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