Graphical Linear Algebra by Pawel Sobocinski.
From Episode 1, Makélélé and Linear Algebra.
Linear algebra is the Claude Makélélé of science and mathematics. Makélélé is a well-known, retired football player, a French international. He played in the famous Real Madrid team of the early 2000s. That team was full of “galácticos” — the most famous and glamorous players of their generation. Players like Zidane, Figo, Ronaldo and Roberto Carlos. Makélélé was hardly ever in the spotlight, he was paid less than his more celebrated colleagues and was frequently criticised by fans and journalists. His style of playing wasn’t glamorous. To the casual fan, there wasn’t much to get excited about: he didn’t score goals, he played boring, unimaginative, short sideways passes, he hardly ever featured in match highlights. In 2003 he signed for Chelsea for relatively little money, and many Madrid fans cheered. But their team started losing matches.
The importance of Makélélé’s role was difficult to appreciate for the non-specialist. But football insiders regularly described him as the work-horse, the engine room, the battery of the team. He sat deep in midfield, was always in the right place to disrupt opposition attacks, recovered possession, and got the ball out quickly to his teammates, turning defence into attack. Without Makélélé, the galácticos didn’t look quite so galactic.
Similarly, linear algebra does not get very much time in the spotlight. But many galáctico subjects of modern scientific research: e.g. artificial intelligence and machine learning, control theory, solving systems of differential equations, computer graphics, “big data“, and even quantum computing have a dirty secret: their engine rooms are powered by linear algebra.
Linear algebra is not very glamorous. It is normally taught to science undergraduates in their first year, to prepare for the more exciting stuff ahead. It is background knowledge. Everyone has to learn what a matrix is, and how to add and multiply matrices.
I have only read the first three or four posts but Pawel’s post look like a good way to refresh or acquire a “background” in linear algebra.
Or as I am fond of saying, “if you let me pick the data or the algorithm, I can produce a specified result, every time.”
Bear that in mind when someone tries to hurry past your questions about data, its acquisition, processing before you saw it, and/or wanting to know the details of an algorithm and how it was applied.
There’s a reason why people want to gloss over such matters and the answer isn’t a happy one, at least from the questioner’s perspective.
Refresh or get an background in linear algebra!
The more you know, the less vulnerable you will be to manipulation and/or fraud.
I first saw this in a tweet by Algebra Fact.