Related papers: Classification of squared normal operators on unit…
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
A holomorphic map from the complex line to a complex projective space is called normal (a. k. a. Brody curve) if it is uniformly continuous from the Euclidean metric to the Fubini--Study metric. The paper contains a survey of known results…
We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis when the phase contributed by each path is described by a quadratic form over…
Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…
We give a canonical form of m-by-2-by-2 matrices for equivalence over any field of characteristic not two.
This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support…
We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.
The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
One can view contraction operators given by a canonical model of Sz.-Nagy and Foias as being defined by a quotient module where the basic building blocks are Hardy spaces. In this note we generalize this framework to allow the Bergman and…
A positive-definite integral quadratic form is called regular if it represents every positive integer which is locally represented. In this article, we classify all regular diagonal quadratic forms of rank greater than 3.
Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over finite fields of characteristic not 2 and over finite…
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 a square complex matrix and $z$ a complex number. The distance, with respect to the spectral norm, from $A$ to the set of matrices which have $z$ as an eigenvalue is less than or equal to the distance from $z$ to the spectrum of…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…
We present two new canonical forms for real congruence of a real square matrix $A$. The first one is a direct sum of canonical matrices of four different types and is obtained from the canonical form under $^*$congruence of complex matrices…
The question of matrix similarity is a classical one in linear algebra. For a field $\mathbb{F}$ and some positive integer $n \in \mathbb{N}$, one may consider the following problems: 1. Given two matrices $A, B \in \mathrm{GL}(n,…