Linear transformations of a finite field

Digraphs of finite linear transformations

If T is a function from a finite set V to itself, we form the digraph D of T as follows. It has V for its vertex set, and there is an arc from x to T (x) for each x E V. Here we answer the following question. Given a finite field F, which digraphs arise as digraphs of a linear transformation from some finite dimensional vector space over F to itself?

On One-Sided Ideals of Rings of Linear Transformations

On fractionally linear functions over a finite field

In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

Linear Transformations

The n×m matrix AT obtained by exchanging rows and columns of A is called the transpose of A. A matrix A is said to be symmetric if A = AT . The sum of two matrices of equal size is the matrix of the entry-by-entry sums, and the scalar product of a real number a and an m× n matrix A is the m× n matrix of all the entries of A, each multiplied by a. The difference of two matrices of equal size A a...

Finite supersymmetry transformations

We investigate simple examples of supersymmetry algebras with real and Grassmann parameters. Special attention is payed to the finite supertransformations and their probability interpretation. Furthermore we look for combinations of bosons and fermions which are invariant under supertransformations. These combinations correspond to states that are highly entangled. ∗ On leave from Institute for...