# Vectors and linear transformation for ML

I am unable to understand or visualize the concepts of vectors and linear transformation for ML. I need thorough explanation on these topics. I tried to find it on google, I searched for it on chatgpt but I am still unable to get the core concept of vector and linear transformation, and I also need to know why and how these concepts are useful for Machine learning.

I am not sure exactly if you want explanations about vectors and explanations about linear transformations or you want to understand vectors and linear transformations.

A linear transformation is basically a function that will take as an input one vector and output another vector. It must satisfy some rules, but the idea is that we can look at linear transformations as a way of “move” vectors in the vector space. For instance, the linear transformation T:\mathbb{R}^2 \rightarrow \mathbb{R}^2 defined by T(v) = 10v, where v = (x,y), x,y \in \mathbb{R} is any vector in the plane.

So, what does this linear transformation do? Well it takes any vector from the plane and stretches it by a factor of 10. This is essentially what a linear transformation does.

Well, one very interesting thing is that there is a one-to-one correspondence between linear transformations and matrices. So, for any linear transformation T, there is a matrix M that represents that linear transformation and, conversely, for any matrix M, it defines a linear transformation T.

So, studying linear transformations is very useful because then we are studying matrices, and basically everything we do nowadays is related to matrices.

I hope that helps.

Cheers,
Lucas

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Thank you .
You explained those topics in easy way. Now i am getting those topics.
I need a suugestion on books. I want a book for maths and for ML, will you suggest me the best book that explain every topic of Maths and ML in very easy way or tell me the books you have used while you were studying ML.