A Linear transformation acts on a vector by shifting it into another coordinate system or vector space. Combining these, we can have a set of matrix multiplications that acts as a single transformation from one vector space to another.

By definition, a linear transformation is a transformation that obeys the two rules

\begin{align} T(\vec{x+y}) =T(\vec{x})+T(\vec{y}) \\ T(a\vec{x}) = aT(\vec{x}) \end{align}

In this section, however, we explore the combination of linear transformations to achieve another linear transformation that may be slightly more computationally difficult.

It graphically looks something like this


*credit for the image from our Linear Algebra Textbook

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