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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Expert Answer

Arnold Odonnell
Answered 2020-11-11 Author has 109 answers
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: XX
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:RnRm satisfying
T(u+v)=T(u)+T(v)
And
T(cu)=cT(u)
For all vector u, v in Rn and all scalars c.
Properties of the linear transformation
Let T:RnRm be a linear transformation. Then:
1) T(0)=0
2. For any vector v1, v1, v2, v3,.vk  Rn and scalars c1, c2, c3, ck
 T(c1v1+ c2v2 + c3v3 + . + ckvk)=c1T(v1) + c2T(v2) + c3T(v3) + .. + ckT(vk)
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.
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