Linear Transformation

Linear transformation is the most important topic in the algebra chapters in mathematics. Linear transformation in mathematics is a rule for changing one figure shape (or matrix or vector) into another by using a formula with a specified format. This format must be a linear combination, in which the original components are modified through the formula of ax + by to form the coordinates of the transformed figure. Stretching it or compressing it, and rotating it. All the transformation has an inverse.
Algebra Linear Transformation

In this linear transformation section we are going to take look at a special kind of function that the study of Linear Algebra and has many applications in fields of mathematics, physics and as well as the engineering field. This basic definitions and facts are combined with this kind of function. We are looking for more number of examples.

Examples on Linear Transformations:

Here we shall solve two examples for Algebra Linear transformation,

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Example1: Zero transformation:

Given: the zero transformation is the transformation T: Sn -> Sm that maps every vector in this format as y in Sn to the zero vectors in Sm, which is T(y) = 0.

Solution:

This is the zero matrix problem so let us take m*n is zero matrix,

And then the matrix induced by this linear transformation is the m*n is zero matrix, 0 matrix is since,

T(y) = T0 (y) = 0y = 0

There fore, to make it clear form of this matrix is, using the zero transformation for matrix, and we are usually denoted by this in T0 (y).

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Example 2: Identity transformation:

Given: the identity transformation is the transformation T: Sn -> Sn  ( both are Sn  because of identity transformations) that maps every vector in this form as y itself to the identity. Which is T(y) = y.

Solution:

Then the matrix induced by this transformation is the n*n matrix (this is identity matrix), so that I n since,

T(y) = Ti (y) = In y = y

There fore, to make it formation of identity transformation is Ti (y) to make clear for this, and we are usually denoted by this in Ti (y).