User:Peter Stalin

Introduction

Hi.

I'm just a mathematics student. I don't plan to make any major edits or articles, I just want a place to have my small edits be counted up as random contributions.

Well, unless some major mathematical topic is missing.

Thanks, Peter Stalin 04:33, 27 March 2007 (UTC)

Preparing up a complete set of residues mod m page

Here's an outline before I start making the article later this week:

-Definition

-Representations --Examples of general representations --Least Absolute residues --Least Positive residues

-Some theorems

-Reduced residue classes

-Some theorems of this too

I still need someplace to mention the 'residue equivalence class' and the applications to group theory in this outline. Peter Stalin 14:13, 28 March 2007 (UTC)

Making a redirect Muller-Traub

Another outline

I don't feel like doing this atm:

In [linear algebra], a matrix $A\in \mathbb {C} ^{n\times n}$ has a displacement rank r if it satisfies a (Sylvester) displacement equation

$EA-AF=GH^{*}$

Where $G,H\in \mathbb {C} ^{n\times r}$ and $E,F$ are called displacement matrices.

Such matrices are useful in defining and categorizing other structured matrices, for example, we can categorize the various matrix structures of the resultant matrix A by the following choices for E,F,G and H

Structure	E	F	G	H
Cauchy Matrix	D_t	D_s	g	h
Cauchy Matrix	D_t	D_s
Cauchy Matrix	D_t	D_s

Where $g,h$ are vectors, $D_{t},D_{s}$ are diagonal matrices,