Related papers: Canonical Forms of Matrices Determining Analytical…
We give a canonical form of m-by-2-by-2 matrices for equivalence over any field of characteristic not two.
We consider a new class of matrices associated to a real square matrix $A$ and to a vector $\vec{c} \in \{-1,1\}^n$ such that $c_1=1$ by using a map $\varphi_{\vec{c}}$ which turns out to be a conjugation of a matrix $A$ by a signature…
A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…
We define the notion of the canonical module of a complex. We then consider Serre's conditions for a complex and study their relationship to the local cohomology of the canonical module and its ring of endomorphisms.
Let $B$ be some invertible Hermitian or skew-Hermitian matrix. A matrix $A$ is called $B$-normal if $AA^\star = A^\star A$ holds for $A$ and its adjoint matrix $A^\star := B^{-1}A^HB$. In addition, a matrix $Q$ is called $B$-unitary, if…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…
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.
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…
In this paper, we give the complete structures of the equivalence canonical form of four matrices over an arbitrary division ring. As applications, we derive some practical necessary and sufficient conditions for the solvability to some…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian…
Given a Morse function f on a closed manifold M with distinct critical values, and given a field F, there is a canonical complex, called the Morse-Barannikov complex, which is equivalent to any Morse complex associated with f and whose form…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
In this paper we use matrices, whose entries satisfy certain linear conditions, to obtain composition identities $f(x_i)f(y_i)=f(z_i)$, where $f(x_i)$ is an irreducible form, with integer coefficients, of degree $n$ in $n$ variables ($n$…
The problem of classifying modules over a tame algebra A reduces to a block matrix problem of tame type whose indecomposable canonical matrices are zero- or one-parameter. Respectively, the set of nonisomorphic indecomposable modules of…
The implicit signature k consists of the multiplication and the ({\omega}-1)-power. We describe a procedure to transform each {\kappa}-term over a finite alphabet A into a certain canonical form and show that different canonical forms have…
Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith…
We discuss the notion of matrix model, $\pi:C(X)\to M_K(C(T))$, for algebraic submanifolds of the free complex sphere, $X\subset S^{N-1}_{\mathbb C,+}$. When $K\in\mathbb N$ is fixed there is a universal such model, which factorizes as…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…