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| Topic | Am I the only one who finds linear algebra harder than integral calculus? |
| Anteaterking 02/07/18 4:38:55 PM #22: | Sad_Face posted... Absolutely not. I have no clue what you're talking about. Please, edumacate me. So it's sometimes interesting to consider the things that are fixed by a transformation. For example, if I have a transformation f(x)=4x, the point x=0 is the only fixed point (since f(0)=0). In higher dimensions, like with vector spaces it would be like saying that a linear transformation defined by a matrix fixes a certain point (or the vector from the origin to that point). Eigenvectors are an extension of that, where instead of saying "I want to know what points (vectors) are fixed by this transformation" you instead say "I want to know which vectors just stretch or contract, but don't change where they are pointing". So say for some matrix M, [1,2] is an eigenvector with eigenvalue 2. That means when you apply your transformation M to the vector [1,2], it becomes [2,4]. It was the equivalent of just multiplying each coordinate by 2, so it's pointing in the same direction , just longer. --- ... Copied to Clipboard! |
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