In my previous blogs I talked about Linear Transformations and how can we find the transformation matrix of a linear transformation. In this blog we will try to understand how to translate basis vectors between different coordinate systems with the

It is important to always think of a matrix as a representation of the transformed standard basis vectors rather than just thinking about a matrix as a rectangular array of random real numbers. With this thought, matrix multiplication can be

The transformation matrix is a representation of the transformed standard basis vectors. For example, in a 2-dimensional coordinate system if the transformed coordinates of the unit vector are, and that of unit vector are, These two basis vectors can be

What is a Linear Transformation? It is a function (the word ‘transformation‘ means the same thing as the word ‘function‘) which takes vectors as inputs and produces vectors as outputs. Linear transformation is also called ‘Linear Map‘ or ‘Linear Mapping‘.