## You are here

HomeThe Rational Matrices editors

## Primary tabs

# The Rational Matrices editors

## Group information

Members: ProfHasan (see full roster)Content: (see full list)

Type: Team

Request group membership

Editors of the ’The Rational Matrices’ object.

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Comments

## Division of Matrices

In this study, we deal with functions from the square matrices to square matrices, which the same

order. Such a function will be called a linear transformation, defined as follows:

Let Mn(R) be a set of square matrices of order n, n ϵ S, and A be regular matrix in Mn(R), then the special

function

TA: Mn(R) → Mn(R)

X T X A X

A

is called a linear transformation of Mn(R) to Mn(R) the following two properties are true for all X,Y ϵ Mn(R), and

scalars α ϵ R:

i. TA (X+Y) = TA(X) + TA(Y). (We say that TA preserves additivity)

ii. TA(αX)= αTA(X) (We say that TA preserves scalar multiplication)

In this case the matrix A is called the standard matrix of the function TA.

Here, we transfer some well known properties of linear transformations to the above defined elements in the set

all { TA: A regular in Mn(R)} [1]

## Division of Matrices

## Division of Matrices

## Division of Matrices

## Division of Matrices

http://jsaer.com/download/vol-3-iss-5-2016/JSAER2016-03-05-101-104.pdf

## On Measurement Assessment and Division Matrices

http://jsaer.com/download/vol-3-iss-6-2016/JSAER2016-03-06-233-237.pdf