Florian Bünger

A matrix-decomposition theorem for GLn(K)

Abstract Given an arbitrary commutative field K , n∈ N ⩾3 and two monic polynomials q and r over K of degree n−1 and n such that q (0)≠0≠ r (0). We prove that any non-scalar invertible n×n matrix M can be written as a product of two matrices A and B , where the minimum polynomial of A is divisible by q and B is cyclic with minimum polynomial r . This result yields that the Thompson conjecture is true for PSL n ( F 3 ) , n∈ N ⩾3 , and PSL 2n+1 ( F 2 ) , n∈ N . If G is such a group, then G has a conjugacy class Ω such that G=Ω 2 . In particular each element of G is a commutator.

Products of symmetries in unitary groups

Abstract Given a regular − -hermitian form on a finite-dimensional vector space V over a commutative field K of characteristic ≠2 such that the norm on K is surjective onto the fixed field of − (this is true whenever K is finite). Call an element σ of the unitary group a symmetry if σ 2 = 1 and the negative space of σ is 1-dimensional. If π is unitary and det π ∈ {1, − 1}, we prove that π is a product of symmetries (with a few exceptions when K = GF 9 and dim V = 2) and we find the minimal number of factors in such a product.

The product of two quadratic matrices

Abstract Let p=(x−β)(x−β −1 )∈K[x] where β 2 ≠β −2 and let V be a finite-dimensional vector space over the field K . A linear mapping M:V→V is called quadratic if p(M)=0 . We characterize products of two quadratic linear mappings.

Standard Integral Table Algebras with a Faithful Nonreal Element of Degree 5

This chapter deals with the classification of standard integral GT-algebras (A,B) with L(B) = 1 {1} and |b| ≥ 4 for all b ∈ B# which contain a nonreal faithful basis element b of degree 5. Starting from this point using the basic identity

Shrink wrapping for Taylor models revisited

\lambda _{xyz} |z|\left\langle {xy,z} \right\rangle = \left\langle {x,z\bar y} \right\rangle = \lambda _{z\bar yx} |x|,x,y,z \in B,

An extended similarity theory applied to heated flows in complex geometries

one can list all possible representations of \( b\bar b \) and b 2 as linear combinations of basis elements (cf. Tables II and III of Subsection 3.3). Assuming that b commutes with \( \bar b \) yields the identity \( \left\langle {b\bar b,b\bar b} \right\rangle = \left\langle {b^2 ,b^2 } \right\rangle \) which reduces the number of these representations (cf. Table III of Subsection 3.3). Then, using various kind of techniques (for example repeated application of the associa- tivity law), each of the reamining cases will be treated separately. In order to state the main result, we introduce the following base of a specific table algebra.

Inverses, determinants, eigenvalues, and eigenvectors of real symmetric Toeplitz matrices with linearly increasing entries

AbstractGiven a regular –-hermitian form on an n-dimensional vector space V over a commutative field K of characteristic ≠ 2 (