# LINEAR TRANSFORMATION HAND WRITTEN NOTE BY DIPS ACADEMY

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

An important special case is when V = W, in which case the map is called a linear operator, or an endomorphism of V. Sometimes the term linear function has the same meaning as linear map, while in analytic geometry it does not.

PARTIAL DIFFERENTIAL EQUATIONS BY RISING STAR ACADEMY

A linear map always maps linear subspaces onto linear subspaces (possibly of a lower dimension); for instance it maps a plane through the origin to a plane, straight line or point. Linear maps can often be represented as matrices, and simple examples include rotation and reflection linear transformations.

REAL ANALYSIS NOTE BY DIPS ACADEMY

In the language of abstract algebra, a linear map is a module homomorphism. In the language of category theory it is a morphism in the category of modules over a given ring.

INTERGRAL CALCULUS HAND WRITTEN NOTE BY DIPS ACADEMY

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