OK, so, I also hate to be "that guy", but, despite the admirable effort put into creating this by the author, I am sad to say I don't see why some people are excited about this... Because unfortunately after just looking at a few pages, I saw lots and lots of error and misleading or plain confusing statements, basically on every single page I looked at closer, which makes me distrust it. Granted, these vary in their severity, but still...

Examples:

- p. 50, definition of a complex vector space, says "
A complex vector space consists of the same set of axioms as the real case, but elements within the vector space are complex.". The vector space does not "consist" of the axiom, it adheres to them. And it makes no sense to say that the "elements" (vectors) are "complex". Rather, that scalars are allowed to be complex, not just real.

- p. 50: definition of a subspace is a mess. To pick just one obvious problem with it: What even are "axioms (a) and (b)"? Perhaps the three unlabeled "axioms" at the top of the page are meant (being closed under addition, additive inverses, and scalar multiplication)? But certainly the third one (axion "(c)"?) needs to be verified, too (whereas the second, about additive inverses, is redundant).

- p. 51 the examples at the top of the page end with mentioning C[a,b], the set of all continuous functions on an interval [a,b]. But then it claims that this is actually not an example, because "it has infinite dimensions". But really this is a perfectly fine vector space (also, we haven't even defined what a "dimension" is yet)

- p. 51, definition of linear independence says "c_1=c_2=c_n=0" which is missing a "=..." before the "=c_n"

- p. 52 the "general vector" given as a column vector doesn't make sense in a general vector space

- p. 53: "Matricis"

- p. 56 "Laprange's theorem" should be "Lagrange's theorem"

- p. 126: "EXPONETIAL"

- p. 167: "Matricies", "Prinicples", "opertaions",

- p. 168: "Determinate"; the formulas for 2x2 and 3x3 matrices implicitly assume a labeling of the entries which is never given, rendering this semi-useless

- one section is titled "MISELANIOUS"

And on page 38, the fields of real and complex numbers, R and C, are introduced as being written with a "blackboard" font (\mathbb), while on page 51 this is not followed (instead, we get \mathcal{R} and plain C). Why even introduce these conventions if they are then not followed?

Sure, many of these are minor and perhaps even "obvious" mistakes. But if you know the matter well enough to spot all of these, maybe you don't need this cheat sheet? Also, as a mathematician myself, my experience is that the number of spelling mistakes in a research paper (or in anything written and submitted by students) is a good first proxy for the quality of the text: if you can't be bothered to even run a spell checker on your text, should I really trust you to have verified all your computations and logical deductions carefully? (And no, I don't apply this to, say, posts here on HackerNews: I hate it when people shoot down a comment, or a twitter post, or whatever, just because it contains typo. But writing a book is a bit of a different affair, isn't it?).

Hence my point that I wouldn't want to suggest this to anybody as a reference. :-(