Math Academy, part 1: My eigenvector embarassment

As a math major, I scored a perfect 100 on my Linear Algebra exam in 1974. However, just two days later, I couldn&#x27;t recall a single thing.<p>A few years ago, with ample free time, I decided to refresh my (nonexistent) memory by watching online linear algebra lectures from various professors. I was surprised by their poor quality. They lacked motivation and intuition. Khan Academy offered no improvement. Then, someone recommended Linear Algebra Done Right (LADR). I read it three times, and by the third iteration, I finally began to appreciate the beauty of the theory. Linear algebra is a purely algebraic theory; visual aids are of limited help. In short, if you have the time, I recommend reading LADR. Otherwise, don&#x27;t bother.

he was a physics and math major and did not know eigenvectors and eigenvalues? i would like to know how is this possible. can someone explain it to me?

Jason Roberts, the founder (and primary coder) of Math Academy, has been podcasting for over 15 years and has been talking about Math Academy and its inspiration, origins, business fundamentals, financial realities, and ambitions on the podcast for many years. A lot of that discussion is distilled in the Math Academy about page (<a href="https:&#x2F;&#x2F;www.mathacademy.us&#x2F;about" rel="nofollow">https:&#x2F;&#x2F;www.mathacademy.us&#x2F;about</a>). If you want to check out the podcast, it&#x27;s here: <a href="https:&#x2F;&#x2F;techzinglive.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;techzinglive.com&#x2F;</a><p>Jason also coined the term &quot;Luck Surface Area&quot; which has since been popularized by a number of others.<p>I haven&#x27;t used Math Academy myself (although it&#x27;s something I intend to try one of these days), but I can safely vouch that Math Academy isn&#x27;t a fly-by-night shallow edtech grift. They&#x27;ve spent a small fortune and thousands of hours developing and refining content and curriculum. Math Academy is a thoughtful, intentional, well-manicured solution.

So you get the explanations and you get the exercises, but can you ask questions?

is MathAcademy that much better that KhanAcademy (which also has a Linear Algebra course and covers eigenvalues of course), which is free? Considering it for my youngest kids, but my eldest (now finished college with a degree in engineering) used Kahn Academy as a high school supplement and it was quite good (this was about 10 years ago). (She didn&#x27;t take the KahnAc LinAlg course -- not sure it was around at that time -- but she did take their calc course and it helped her ace her CalcBC AP test.)

To be honest, I just read the introductory post, and it&#x27;stated there that the author wants to do MVC after finishing LinAlg, which is stated as their goal for end of 2025.<p>As someone that has the same <i>end goal</i> (but probably 2026 for me) - isn&#x27;t it maybe wiser to do MVC before LinAlg?<p>Read the whole thing now, slightly disappointed OP doesn&#x27;t try to tell us what an eigenvector is, based on his current progress.

Math Academy is the best online course I’ve ever done

I hope someone here finds this solution set of mine useful:<p><a href="https:&#x2F;&#x2F;drive.google.com&#x2F;drive&#x2F;folders&#x2F;1JrMp7R4j86tMzHn0Sfa_GMl9ZVXd0Wyj" rel="nofollow">https:&#x2F;&#x2F;drive.google.com&#x2F;drive&#x2F;folders&#x2F;1JrMp7R4j86tMzHn0Sfa_...</a>

I have a fairly similar story to the OP. I have an engineering degree, but that was 25 years ago. I started reading a lot of &#x27;proper&#x27; maths a few years back (abstract algebra, topology etc) and made decent progress, but it never quite stuck. The lack of decent problem sets with answers in so many textbooks is really limiting.<p>Going back through the foundations courses on Mathacademy (I started halfway through Math Foundations II, currently nearing the end of III) has been great. It&#x27;s been surprising how much I&#x27;ve forgotten, but also reassuring how quickly it comes back. My plan is to move on to the more advanced courses with firmer foundations.<p>The focus on answering questions constantly helps me focus, although the multiple choice structure is kind of limiting, if inevitable. It&#x27;s frustrating to have it throw a whole load more questions at you because you missed a minus sign, where a proper teacher would have seen your working and been able to tailor their feedback.

I hope math academy keeps adding more courses because it looks very promising, now it&#x27;s a bit too basic unfortunately.

I cancelled my Math Academy sub because I ran out of 30 minute blocks for SAT problems I would never need. It was too remedial.

Skip to last chapter.<p>&gt; The most notable of these are the synthetic division method for polynomials, the various trigonometric identities, and differentiation of products and quotients of functions.<p>So he learned nothing you already know at 15. Or younger in Asia.<p>I think he forgot his goals because it doesn’t even mention eigenvectors.<p>I am surprised because it is not a difficult thing to understand? It is a vector that when multiplied to a matrix (which in almost all cases would change the direction of the vector), in fact only scales it - and does not change its direction.<p>The scale factor is its eigenvalue.<p>So if you hav [[2,0],[0,3]] this should when multiplied to a vector give you [2x,3y]. But if you supply the vector [1,0] or [0,1] you see that the result multiplies that vector by two. So any multiple of these eigenvectors (e.g. [10,0]) will result in a doubling of the vector.<p>This is not a difficult concept. By any means.

eigenvectors were the only tough part of the linear algebra course i took, i think that&#x27;s b&#x2F;c it&#x27;s quite a bit to learn before you start seeing the point of it. methods like PCA are rely heavily on eigendecompositon and allow you to reduce the dimensions of data...this is useful in all sorts of ways like compression for instance (e.g. getting rid of the dimensions that aren&#x27;t very meaningful).