We predict basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.

Linear algebra is a fundamental discipline underlining anything one can do with Math. From Physics to machine learning, probability theory (ex: Markov chains), you name it. Irrespective of what you’re doing, linear algebra is all the time lurking under the covers, able to spring at you as soon as things go multi-dimensional. In my experience (and I’ve heard this from others), this was on the source of an enormous shock between highschool and university. In highschool (India), I used to be exposed to some very basic linear algebra (mainly determinants and matrix multiplication). Then in university level engineering education, every subject rapidly appears to be assuming proficiency in concepts like Eigen values, Jacobians, etc. such as you were speculated to be born with the knowledge.

This blog is supposed to offer a high level overview of the concepts and their obvious applications that exist and are vital to know on this discipline. So that you just at the least know what you don’t know (if anything). Its also an excuse to gather resources and links so people can dig deeper into the rabbit hole.

As mentioned within the previous section, linear algebra inevitably crops up when things go multi-dimensional. We start off with a scalar, which is just a variety of some sort. For this text, we’ll be considering real and sophisticated numbers for these scalars. Normally, a scalar will be any object where the fundamental operations of addition, subtraction, multiplication and division are defined (abstracted as a “field”). Now, we would like a framework to explain collections of such numbers (add dimensions). These collections are called “vector spaces”. We’ll be considering the cases where the weather of the vector space are either real or complex numbers (the previous being a special case of the latter). The resulting vector spaces are called “real vector spaces” and “complex vector spaces” respectively.

The ideas in linear algebra are applicable to those “vector spaces”. Essentially the most common example is your floor, table or the pc screen you’re…