Linear transformations, the heart of linear algebra
A linear transformation is a basic thing that everyone should know to gain insights of linear algebra. But, here is the question, what does linear transformation means actually? Let me introduce our topic today.
Firstly, let's focus on what does transformation means, in a simple term, transformation is the function that takes one input and provides another output after some mathematical calculations or any required procedures. In the case of vectors, it takes some input and produces or spits out some other vectors as an output. So, just think of transformations as a machine that takes one value and after some calculation, it provides you with output. The input may be any numbers, text, graphics depending on the domain of study and the output is according to their respective inputs.
Now, I have mentioned about transformations but what about the linear, why there is a linear word in this?
Well, in linear transformations all the line will be a line or simply saying after some transformations the output must not be any curve or any other shapes except a line. I hope you got it.
Another thing to remember is that, in linear transformations, the origin must be fixed at the center (0,0). If it deviates from the origin it violates the rules of linear transformations.
Linear transformations hence can be defined as the mathematical function that maps an input to output and such output must be centered at the origin and must be a line. If we see other shapes apart from the line and also if the line is not centered at origin we violate the rules of a linear transformation.
Ok, this is just a quick overview of linear transformations. But inside this, there are more things to talk about like matrices, cross-products, determinants, and so on. I might come with new stories including them and will try to explain in an easy way. Thank you.
