Vectors | Chapter 1, Essence of linear algebra

If you actually want to learn linear algebra, don't use this blogpost. It's real weaksauce compared to the wealth of free information and resources available online. Firstly, the real illustrated guide to linear algebra is the youtube series "The Essence of linear algebra" by 3blue1brown[1]. It has fantastic visualisations for building intuition and in general is wildly superior to this, which seems fine but extremely superficial. If you're done with 3b1b and want to take things further, then the go-to is the excellent 18.06SC course by the late and legendary Gilbert Strang. It's amazing, it's free. [2] Still want more? OK now you're talking my language. If you are serious about linear algebra (Up to graduate level, after that you need something else) then you want the book "Linear Algebra Done Right" by Sheldon Axler. It's available for free from the author's website[3] and he has made a bunch of videos to supplement the book. There's also an RTD Math full lecture series[4] that follows the book and he explains each thing in a lot of detail (because Axler goes fast , so it's beneficial to unpack the concepts a bit sometimes). [1] [this video] [2] [link] [3] [link] and [link] [4] [link]

Maybe you would get something out of 3blue1brown's series on linear algebra [1]. It will give you an intuitive, geometric interpretation for concepts such as a vector, a basis, an eigenvalue, a linear transformation, etc. As for why you would want to know these things, well, linear algebra is finding applications all over the place these days. Everything from computer graphics to machine learning is jam-packed with linear algebra. And I'm not just talking about basic concepts such as matrix-vector multiplication. The singular value decomposition has applications in discrete optimization, image compression, the PageRank algorithm [2], computer vision [3], and machine learning [2] [4]. Having said that, you may find it very difficult to understand something like SVD without a firm grounding in the topic of vector spaces, linear transformations, spanning, linear (in)dependence, subspaces, eigenvalues, eigenvectors, diagonalization, and determinants. This is why SVD is one of the last things you learn in a linear algebra course (indeed, it's not covered until lecture 29 of Gilbert Strang's course). Ultimately, it all depends on how relevant these things are to you. I would assume (hope) that because you clicked on this HN discussion that you're interested in learning linear algebra because you think it might be useful to you. [1] [this video] [2] [link] [3] [link] [4] [link]

To answer your main question - "what level of maths" do you need is more about what topics: a couple introductory classes in Calculus, Linear Algebra, and Discrete Mathematics will make that sentence understandable. I'll give some definitions and resources, but think about how you would explain multiplication/division/algebra to a kid. At some point, you just have to work through some problems and the math just makes sense. So I'll explain the terms above, but best bet is to just take a few courses on the topics I mentioned above. Quick definitions: - Exponential: is the constant e to the power of some number. e, like pi, is a ubitiqous constant in mathematics and nature. You run into pi when doing geometry, and e when doing calculus. - A function in mathematics is similar to a function in programming, but not exactly. A course in Discrete Mathematics helps here. - F-apostrophe is notation used in calculus to show the relation of one type of function, called a derivative to another. f and f' are related. How, though, is better explained by taking calculus. - An eigenfunction exists in a system of equations. Think of it like a 'balance' point. Linear Algebra will help make sense of this term. Resources - Essence of Calculus: [link] - Essence of Linear Algebra: [this video] Those 2 video's will do a good job of giving you the 'intuition' behind Calculus and Linear Algebra. Like programming, though, you just have to actually work some problems out by hand for the stuff to sink in. Fo