Notes on linear transformations. I

Notes on the Structure of Linear Transformations

The goal of these notes is to give an accessible introduction to the structure theory of linear transformations. We want to develop enough of the theory for use in differential equations, with only basic linear algebra as a prerequisite. In a following set of notes, we will show how these results can be applied to differential equations. In the rest of the section, we will cover some topics tha...

On One-Sided Ideals of Rings of Linear Transformations

On Linear Polygon Transformations

Linear Transformations on Matrices *

Even in thi s generality , it is clear that .!l' (I , ~) is a multiplicative se migroup with an ide ntity. The invariant I can be a scalar valued fun ction, e.g. , I (X) = det (X) ; or for that matter it can describe a property, e.g., m can equal M" (C) and I (X) can mean that X is unitary , so that we are simply asking for the s tructure of all linear transformation s T that map the unitary gr...

Linear transformations on codes

This paper studies and classifies linear transformations that connect Hamming distances of codes. These include irreducible linear transformations and their concatenations. Their effect on the Hamming weights of codewords is also studied. Both linear and non-linear codes over fields are considered. We construct a family of pure binary quantum codes using these transformations. It is shown that ...