The beauty of Linear Algebra

Linear algebra is the branch of mathematics that concerns linear equations, maps and their representations in vector spaces and through matrices. This technical definition and most proofs, concepts and theorems that we learn hide the visual beauty of linear algebra. My goal in this article is to arouse curiosity so you too can enjoy this subject as much as I do after seeing it what it meant. <h1>Vectors</h1> Vectors can be interpreted differently at some fields. For example, as an arrow, as a list of values, a geometric object etc. For now, think of it as an arrow, but inside of a coordinate system xy (cartesian plan). The tail of the vector sits at the origin of our system. The coordinates of a vector basically is telling us how to get from the tail of the vector to its tip. For example, a vector v = [1, 2] would have its tail on the origin and its tip at (1, 2) in our cartesian plan. It is important to understand that we can do operations with vectors too. For example, we can add the vectors v = [1, 2] and w = [3, 4] . The sum of this vectors is [1 + 3, 4 + 2] = [4, 6] . But what this represent visually? Try to visualize this in your mind: adding two vectors means getting the tail of the second vector, placing it in the tip of our first vector and then creating a new vector that goes from the origin to the tip of our sum. <a href="https://medium.com/@lorenzowbattistela/the-beauty-of-linear-algebra-160de36b680a">Website</a>