Eigenvalues and eigenvectors are one of those things that pop up in a million places because they're so useful, but to recognize where they may be useful you need intuition as to what they're doing.
One of my biggest hurdles learning linear algebra was getting that intuition. This "standard way of explaining scientific things" never built that intuition for me, only forced the mechanics of the computation into pencilized muscle memory.
Don't get me wrong, you need that muscle memory in practice. But without the intuition, your muscle memory is always going to be inferior to a couple commands in matlab. Stuff like this visualization builds the intuitive knowledge -- you see, you explore, you wiggle a few things and see what happens when you go in and out of the sweet spot.
Play (and simulation) is an extremely effective way to build intuition, and one I'd love to see more. These guys are doing an awesome job at these kinds of simulations -- their markov chain one was fantastic too http://setosa.io/ev/markov-chains/
Stuff like this visualization builds the intuitive knowledge -- you see, you explore, you wiggle a few things and see what happens when you go in and out of the sweet spot.
Disagree. The linked article does a very poor job of explaining anything, much less conveying intuition. The lambda values remain even if the 3 points are not collinear, thus contradicting the first part of the article.
Comments
Eigenvalues and eigenvectors are one of those things that pop up in a million places because they're so useful, but to recognize where they may be useful you need intuition as to what they're doing.
One of my biggest hurdles learning linear algebra was getting that intuition. This "standard way of explaining scientific things" never built that intuition for me, only forced the mechanics of the computation into pencilized muscle memory.
Don't get me wrong, you need that muscle memory in practice. But without the intuition, your muscle memory is always going to be inferior to a couple commands in matlab. Stuff like this visualization builds the intuitive knowledge -- you see, you explore, you wiggle a few things and see what happens when you go in and out of the sweet spot.
Play (and simulation) is an extremely effective way to build intuition, and one I'd love to see more. These guys are doing an awesome job at these kinds of simulations -- their markov chain one was fantastic too http://setosa.io/ev/markov-chains/
Disagree. The linked article does a very poor job of explaining anything, much less conveying intuition. The lambda values remain even if the 3 points are not collinear, thus contradicting the first part of the article.