Linear Algebra: a very very very short intro

Chris Catalfo bio photo By Chris Catalfo Comment

What is this thing called Linear Algebra?

I’ve decided to learn linear algebra, so here I am.

What is linear algebra? That’s what we’re here to find out.

I’ll be using various sources to learn, including the Coding the Matrix coursera course, Gilbert Strang’s online course, and other materials I find here and there.

A first taste

Before we dive right in here’s a first taste of what it’s about, as far as I’ve learned so far.

Say we have a list of numbers we need to work with. Maybe a list of numbers indicating dimensions of books, in cm.

It is sometimes convenient to work with this list of numbers such as this as one unit, in which case we can call it a vector of numbers.

Dimension of a vector

The preceding vector has 4 “things in it”, or elements, so we say it is a 4-vector.

Elements of a vector

The elements in this case are real numbers so we can describe the vector as being a vector drawn from , the set of groups of 4 real numbers.

Relating it to programming

Since I’m a programmer I sometimes find it helps to think of things as a programmer might.

In this case let’s think of that age-old staple of computer programming, the list:

[12,10,15,11]

The “elements” of this list would be its consitituents:

12 10 15 11

The “dimension” of this list would be the number of elements in it, in other words, its length:

len([12,10,15,11]) == 4

Coming up

Next we talk about things we can do with vectors such as adding them.