Linear Transformation

Linear transformations or linear maps are an important concept in mathematics, particularly in the fields of linear algebra and functional analysis. A linear transformation can be thought of as a transformation that preserves the operations of addition and scalar multiplication. In other words, a transformation T is linear if for every pair of vectors x and y, the equation T(x + y) = T(x) + T(y) holds true. Similarly, for any scalar c and any vector x, the equation T(cx)=cT(x) should also hold true. This property makes them very useful when dealing with systems of linear equations, matrices, and in many areas of computer graphics, including game development.