相关论文: A recursive parameterisation of unitary matrices
A biunimodular vector of a unitary matrix $A \in U(n)$ is a vector $v \in \mathbb{T}^n\subset\bc^n$ such that $Av \in \mathbb{T}^n$ as well. Over the last 30 years, the sets of biunimodular vectors for Fourier matrices have been the object…
We give a number of algorithms for constructing unitary matrices and tight frames with specialized properties. These were produced at the request of researchers at the Frame Research Center (www.framerc.org) to help with their research on…
Under the exponential parametrization scheme $ m^{\nu}_{ij}\sim r e^{i \theta}$, we propose a \emph{unique} neutrino mass matrix texture that exhibits four correlations among its elements. The mixing scheme obtained from the proposed…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…
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.…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence…
We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to…
We construct renormalised models of regularity structures by using a recursive formulation for the structure group and for the renormalisation group. This construction covers all the examples of singular SPDEs which have been treated so far…
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with the same solutions as a given linear recurrence, and…
The quark mixing matrix is parameterised such that its "Cabibbo substructure" is emphasised. One can choose one of the parameters to be an arbitrarily chosen angle of the unitarity triangle, for example the angle $\beta$ (also called…
Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…
We calculate a two-parameter R-matrix which specialises to the trigonometric R-matrix of the minimal affinisation of the adjoint representation of each of the classical simple Lie algebras so(n) and sp(n).
This paper gives a rigorous proof of a conjectured statistical self-similarity property of the eigenvalues random matrices from the Circular Unitary Ensemble. We consider on the one hand the eigenvalues of an $n \times n$ CUE matrix, and on…
Consider the most general $3 \times 3$ Majorana neutrino mass matrix $\cal M$. Motivated by present neutrino-oscillation data, much theoretical effort is directed at reducing it to a specific texture in terms of a small number of…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
This paper provides a one-line proof of Frequent Directions (FD) for sketching streams of matrices. The simpler proof arises from sketching the covariance of the stream of matrices rather than the stream itself.
We develop a matrix bordering technique that can be applied to an irreducible spectrally arbitrary sign pattern to construct a higher order spectrally arbitrary sign pattern. This technique generalizes a recently developed triangle…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
The mass matrices of charged fermions have a simple structure if expressed in powers of the small parameter sigma=(m_c/m_t)^{1/2}. It is suggested that the mass matrix of the three heavy neutrinos occuring in grand unified theories can be…