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

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In mathematics, a transformation is a f that maps a set X to itself, i.e,f:X→X. 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:Rn→Rm satisfying T(u+v)=T(u)+T(v) and T(cu)=cT(u) for all vectors u,v∈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 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.

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

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