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Skip to last chapter. > The most notable of these are the synthetic division method for polynomials, the various trigonometric identities, and differentiation

Skip to last chapter. > The most notable of these are the synthetic division method for polynomials, the various trigonometric identities, and differentiation of products and quotients of functions. So he learned nothing you already know at 15. Or younger in Asia. I think he forgot his goals because it doesn’t even mention eigenvectors. 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. The scale factor is its eigenvalue. 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. This is not a difficult concept. By any means.

fransje26 2y ago
Hooray! You managed to explain it as dryly and as poorly as any other linear algebra book or course out there. Now, do the part with the explanation of what it actually means for a (physical) system to have eigenvalues, and what it tells you about the response of such a system to external or intensive inputs, or how to change such a system to targeted a certain response.
- pinoy420 2y ago
  If you find that anything besides a poor dry explanation, that is on you. I am sorry this enrages you. Eigenvalues in an oscillating system describe its resonant frequencies. Its eigenvectors can describe motion at that certain resonant frequency. Imagine a bridge. If wind or traffic match a resonant frequency (eigenvalue) it would be dangerous. Engineers can redesign it to change the corresponding eigenvector and shift the eigenvalue (its resonant frequency for that mode of oscillation) to a safer range. See that bridge in London.

fransje26 2y ago

Hooray! You managed to explain it as dryly and as poorly as any other linear algebra book or course out there. Now, do the part with the explanation of what it actually means for a (physical) system to have eigenvalues, and what it tells you about the response of such a system to external or intensive inputs, or how to change such a system to targeted a certain response.

pinoy420 2y ago
If you find that anything besides a poor dry explanation, that is on you. I am sorry this enrages you. Eigenvalues in an oscillating system describe its resonant frequencies. Its eigenvectors can describe motion at that certain resonant frequency. Imagine a bridge. If wind or traffic match a resonant frequency (eigenvalue) it would be dangerous. Engineers can redesign it to change the corresponding eigenvector and shift the eigenvalue (its resonant frequency for that mode of oscillation) to a safer range. See that bridge in London.