Introduction to Linear Algebra
What is Linear Algebra?
Linear algebra is the branch of mathematics concerned with vectors and matrices, their linear combinations and operations acting upon them.
We will learn linear algebra for machine learning and not in perspective of theoretical linear algebra instead applied linear algebra. We will use python to make it a practical series and we will also use manim for visualising geometric perspective for most of the concepts.
One thing that you should always remember:
Linear Algebra is all about vectors and matrices and how to use them.
What is a Vector?
A vector is an ordered list of numbers that can be arranged in a column or in a row:
Column Vector:
Row Vector:
What is a Matrix?
A matrix is a spreadsheet of numbers. In pure maths, we can have infinitely long vectors and matrices can be of infinite number of rows and columns. But in this series, we are learning this for machine learning and computer science.
That’s why we will discuss about vectors and matrices that have a finite number of rows and columns
Algebraic and Geometric Interpretation of Vectors and Matrices
Vectors and matrices have an algebraic interpretation like above example and vectors and matrices have geometric interpretations that gives us a real world understanding of vectors and matrices.
In this series, we will see concepts from both these interpretations and understand linear algebra very clearly and visualise their concepts and ideas.
This was just an introduction to the series. In the next article, we will see what a vector really is in both the algebraic and geometric interpretation
Till then goodbye, happy learning.