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The Rational Matrices editors

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The Rational Matrices editors

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Editors of the ’The Rational Matrices’ object.


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ProfHasan's picture

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]

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