# Define Transformation. Write down the properties of Linear transformation and rotational transformation.

Falak Kinney 2020-11-10 Answered
Define Transformation.
Write down the properties of Linear transformation and rotational transformation.
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Arnold Odonnell
Step 1: Transformation
In mathematics, a transformation is a function f (usually with some geometrical underpinning) that maps a set X to itself, i.e f: $X\to X$
Examples:
(1) Linear transformation of vector spaces
(2) Geometric transformation
More generally, a transformation in mathematics means a mathematical function (i.e map or mapping). A transformation can be an invertible function from a set X to itself or X to another set Y.
Step 2: Linear transformation
A linear transformation is a transformation $T:{R}^{n}\to {R}^{m}$ satisfying
$T\left(u+v\right)=T\left(u\right)+T\left(v\right)$
And
$T\left(cu\right)=cT\left(u\right)$
For all vector u, v in ${R}^{n}$ and all scalars c.
Properties of the linear transformation
Let T$:{R}^{n}\to {R}^{m}$ be a linear transformation. Then:
1) $T\left(0\right)=0$
2. For any vector and scalars

Step 3
A rotational transformation is a transformation that turns a figure around a given point called the center of the rotation. The size and shape of the figure don’t change after rotation.
Properties of rotational transformation
1. A rotation maintains the length of segments.
2. A rotation maintains the measure of angles.
3. A rotation maps a line to line, ray to ray, a segment to a segment, and an angle to an angle.