Related papers: On the Odd Unitary Analogue of Gram-Schmidt Proces…

The Gram-Schmidt process of L.N. Vaserstein for making an elementary matrix symplectic yields a nice set of generators for the odd sized elementary group.

In this article we define a set of matrices analogous to Vaserstein-type matrices which was introduced in the paper `Serre's problem on projective modules over polynomial rings and algebraic K-theory' by Suslin-Vaserstein in 1976. We prove…

In this paper we study odd unimodal and odd strongly unimodal sequences. We use $q$-series methods to find several fundamental generating functions. Employing the Euler--Maclaurin summation formula we obtain the asymptotic main term for…

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors, matrices, etc) into an orthonormal basis (a set of orthogonal, unit-length vectors, bi or tri dimensional matrices). The…

The Gram-Schmidt algorithm produces a pairwise orthogonal set from a linearly independent set of vectors in an inner product vector space V. We give a linear algorithm that constructs vectors with the same span and which have pairwise the…

For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central.…

V. I. Arnold [Russian Math. Surveys 26, no. 2, 1971, 29-43] constructed smooth generic families of matrices with respect to similarity transformations depending smoothly on the entries of matrices and got bifurcation diagrams of such…

This paper presents an algorithmic method for generating random orthogonal matrices \(A\) that satisfy the property \(A^t S A = S\), where \(S\) is a fixed real invertible symmetric or skew-symmetric matrix. This method is significant as it…

Matrix generators for the general and special linear groups, the symplectic groups and the general and special unitary groups over finite fields. For the most part the generators have been obtained by translating Steinberg's generators for…

The sister of Eisenstein-Picard modular group was described in [8]. In this paper we give a similar definition of the sister of the Euclidean-Picard modular group and find its generators by using a geometric method.

It is shown that the characteristic vector field associated to a first order PDE has the same form of an infinitesimal generator of an odd-symplectic transformation with contact Hamiltonian the given PDE. It is considered under which…

We define a new variety of loops we call $\Gamma$-loops. After showing $\Gamma$-loops are power associative, our main goal will be showing a categorical isomorphism between Bruck loops of odd order and $\Gamma$-loops of odd order. Once this…

Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system $\mathsf{BC}_\ell$ and may be constructed by…

We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of their corresponding Grassmannians realized as involution…

For an odd quadratic space $V$ of Witt index $\geq 3$ over a commutative ring with pseudoinvolution, we classify the subgroups of the odd unitary group $U(V)$ that are normalized by the elementary subgroup $EU_{(e_1,e_{-1})}(V)$ defined by…

There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This…

We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary…

A parametrization, given by the Euler angles, of Hermitian matrix generators of even and odd-degenerate Clifford algebras is constructed by means of the Kronecker product of a parametrized version of Pauli matrices and by the identification…

I show how applying a symplectic Gram-Schmidt orthogonalization to the normalizer of a quantum code gives a different way of determining the code's logical operators. This approach may be more natural in the setting where we produce a…

We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring $R[X]$, over a commutative ring $R$ in which 2 is invertible, as a product of an…