# Become a Linear Algebra Expert

Vectors are mathematical entities that have different meanings, but all connect together one way or the other.

The most common definition of a vector is that it has direction and magnitude in space. In linear algebra, the magnitude and direction represents the the direction between points.

Vectors can also represent a group of numbers, just like how one would use in programming. This set of number can be geometrically interpreted as a set of point in space.

In this course, vector is represented as a vertical column consisted of numbers. The vector has to have an \textbf{arrow} on top, indicating that it is a vector

$$\vec{a} = \begin{bmatrix}a_1\\a_2\end{bmatrix}$$

Where the numbers inside the vectors are called the \textbf{components} of the vector. These components represent the position that it has on each axis in space. Although only up to 3rd dimension can be visualized, dimension above 3 has axis as well.