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

Ayaana Buck 2020-12-03 Answered
Define Transformation? Write down the properties of Linear transformation and rotational transformation.
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sweererlirumeX
Answered 2020-12-04 Author has 91 answers

In mathematics, a transformation is a f that maps a set X to itself, i.e,f:XX.
Examples:
(1). Linear transformation of vector space
(2) Geometric transformation
More generally, a transformation in mathematics means a mathematical function. A transformation can be an invertible function from a set X to itself or X to another set Y
A linear transformation is a transformation T:RnRm satisfying T(u+v)=T(u)+T(v) and T(cu)=cT(u)
for all vectors u,vRn 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 y1,v2,v3,v4,....v,Rn
and scalars c1,c2,...ck,
T(c1v1,+c2v2,+...+ckvk)=c1T(v1)+c2T(v2)+...+ckT(vk)
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 maintain 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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