Maximal Unimodular Systems of Vectors

On Completing Unimodular Polynomial Vectors of Length Three

It is shown that if R is a local ring of dimension three, with ¿ € R , then a polynomial three vector (vQ(X), vx(X), v2(X)) over R[X] can be completed to an invertible matrix if and only if it is unimodular. In particular, if 1/3! € J! , then every stably free projective R[XX, ... , .Y„]-module is free.

Unimodular triangulations of simplicial cones by short vectors

Article history: Received 23 January 2016 Available online xxxx

First-order optical systems with unimodular eigenvalues.

It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the separable fractional Fourier transformer are related by means of a similarity transformation. More...

Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules

In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

Maximal coupling of empirical copulas for discrete vectors