Had a go at learning some linear algebra through a great Khan Academy course today. Vectors seem to turn up in my work constantly and its something I’ve kind of gotten used to through exposure, but I don’t really have a solid grasp on the maths. Hopefully after this course I will!

All images are from the course, which can be found here.

**What is a Vector?**

A vector is a list of numbers that represents a direction and length in 2D or 3D space.

**Vector Addition**

Adding two vectors together is like placing the second vector at the end of the first, and then drawing a line between the origin and the end of the second vector.

**Scalar Multiplication**

When we multiply a vector by a single number, we essentially stretch it out by that amount, or scale it. Therefore in linear algebra numbers tend to be called scalars.

**Bases Vectors **

The base vectors are the vectors that all others in our coordinate system are derived from. For example, the most common base vectors are î and ^ j (known as unit vectors) which are 1 in the x and y direction.

Any time we have a vector, it is basically a scaled version of the base vector.

**Linear Combination and Span**

The linear combination of two vectors is anytime a vector is scaled and added. The span of a set of vectors is all of the possible vectors that can be made using the linear combination. For example, with î and ^ j, the linear combination is made up of all possible 2D vectors, but if we were to use the vectors [1, 0] and [3,0] the linear combination would be all possible vectors on one line. If the vectors were both 0, the only linear combination would be 0.