Linear algebra is like the Swiss Army knife of science, and it is used in pretty much all areas of science for modelling. I assume you remember high school math

Linear algebra is like the Swiss Army knife of science, and it is used in pretty much all areas of science for modelling. I assume you remember high school math functions, and how useful they are to help us describe input-output relationships between real number inputs and real number outputs. Now imagine the inputs are vectors and the outputs are vectors too, in other words we would need vector-functions. Many problems in math, science, computing, economics, biology — you name it — are of this multidimensional nature, so the more you know about vector functions the better models you can build. As you can imagine describing arbitrary input-output relationships between high-dimensional spaces is quite complicated. Think of all the possible ways that a vector input vec{x} = [x1,x2,...xn] can affect the coefficients of a vector output vec(y) = [y1,y2,...ym]. If you allow arbitrary functions like quadratics, sine, cosine, exp, etc. there would be way too many different ways to map vec(x) to vec(y). Too many ways... This is where the "linear" part of linear algebra comes in. Instead of arbitrary input output transformations vec(x) --> vec(y), what if we restrict oursleves only to relationships where the output yi is some linear combination of the inputs x1 x2 .. xn, where linear combination means y1 = m11*x1 + m12*x2 + ... + m1n*xn in other words, take the outputs are equal to the inputs times some proportionality coefficients mij. The other output coefficients y2...ym are computed in the same way with different coefficients y2 = m21*x1 + m22*x2 + ... + m2n*xn ... ym = mm1*x1 + mm2*x2 + ... + mmn*xn thus the overall map vec(x) --> vec(y) has a total of m*n coefficients mij. This map between inputs vec(x) and outputs vec(y) is the vector-equivalent of the single-variable function y=mx (proportionality relationship, or line with slope m passing through the origin if your prefer to think of it geometrically). We call these maps "linear transformations" and they have really nice properties. If you study linear algebra you'll learn all about them. Computationally (usefully), geometrically (Whoooa moments), and theoretically (knowledge buzz). And that's just the math part! Once you start to look into applications, it goes really far... Others in this thread have already mentioned numerous areas of applications in CS areas, and it's the same in biology, chemistry, economics, etc. TL;DR: linear algebra is good stuff! PS: Here is a short video where I explain more about why linearity [normally written as f(ax1+bx2) = af(x1)+bf(x2)] is so important: https://github.com/minireference/noBSLAnotebooks#ch2-linearity https://github.com/minireference/noBSLAnotebooks#ch2-lineari...