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

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

Arnold Odonnell · Accepted Answer

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→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:Rn→Rm 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:Rn→Rm 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.

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

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