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

Define Transformation.
Write down the properties of Linear transformation and rotational transformation.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

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.