The PDF is accompanied by this video.
Here’s an interesting question: take a 2-dimensional sphere inside of a 3-dimensional space. Any rotation you can think of, always leaves 2 points fixed . They are the only 2 points that don’t move. Now, increase the dimensions by 1: imagine a 3-dimensional sphere sitting inside of a 4-dimensional space. Do you think that the same things must still be true here? Or is it possible to rotate it such that every single point of the sphere moves?
You know, this is exactly the kind of question where our 3D intuition fails. And if you want to get insights on what happens in higher dimensions, you need to rewire your brain. The best way to do it is with the tools of linear algebra. Let’s get started.
Get very useful info that is unavailable anywhere else in this Learning Material on
This PDF offers a clear overview of the core ideas of linear algebra. It will help you build the mathematical language needed to understand vectors, vector spaces, linear transformations, matrices, and fundamental concepts such as eigenvalues and eigenvectors. If you are serious about learning linear algebra, this is an ideal resource for developing a rigorous foundation grounded in visual intuition and concrete examples. The included exercises, with detailed solutions, will help you test your understanding and practice the material on your own.
In any case, if you don’t have the means, we always have our free videos. Thanks again!
DiBeos 
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