Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically ...

We complete all local spinor norm computations for quater-nionic skew-hermitian forms over the field Qof rational num-bers. This can be used to compute the number of classes in a genus of skew-hermitian lattices of rank ...

We characterize the hermitian levels of quaternion and octonion algebras and of an 8-dimensional algebra D over the ground field F, constructed using a weak version of the Cayley-Dickson double process. It is shown that ...

We characterize the hermitian levels of quaternion and octonion algebras and of an 8-dimensional algebra D over the ground field F, constructed using a weak version of the Cayley-Dickson double process. It is shown that ...

We introduce the projective Hermite constant for positive definite binary hermitian forms associated with an imaginary quadratic number field K. It is a lower bound for the classical Hermite constant, and these two constants ...

In this paper it is proved that hermitian forms over quaternion division algebras over local fields of characteristic two are classified by their dimension and discriminant.

The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal {k+1}-potent matrix are considered. First, we study the existence of the solutions ...