4 ms·

If you are not speaking in jest (I strongly suspect you are), knowledge of linear algebra is one of the biggest bang for buck one can get as an investment in ma

by srean 8mo ago

If you are not speaking in jest (I strongly suspect you are), knowledge of linear algebra is one of the biggest bang for buck one can get as an investment in mathematical knowledge. So humble and basic a field. So wide it's consequences and scope.

Sharlin 8mo ago
Their point was that "familiarity" apparently means different things for different people :P Someone using linalg in computer graphics applications may say they're familiar with it even though they've never heard the term "eigenvector". I'm not actually sure about what you mean – how does repeated multiplication reveal eigenvectors?
- srean 8mo ago
  Consider a diagonalizable matrix A. For example, a real symmetric matrix. Start with any vector b and keep multiplying it with A. A A A ... A b The vector that the result will converge to is a scaled version of one of the eigenvectors of the matrix A. But which one ? The one with the largest eigenvalue among all eigenvectors not orthogonal to b. https://en.wikipedia.org/wiki/Power_iteration https://en.wikipedia.org/wiki/Power_iteration
  - Sharlin 8mo ago
    Ah… that "diagonalizable" is doing some heavy lifting there! I was wondering how exactly you’re going to make, say, a rotation matrix to converge anything to anything that’s not already an eigenvector. And rotation matrices certainly aren’t degenerate! Though apparently non-diagonalizable matrices can be called defective which is such a dismissive term :( Poor rotation matrices, why are they dissed so?!
    - srean 8mo ago
      Love them, those rotation matrices. Take logarithm of the eigenvalues and you get back the angle. This to me had solidified the notion that angles are essentially a logarithmic notion ... Made more rigorous by the notion of exponential maps
CoastalCoder 8mo ago
My first sentence was in jest. I've used LA for various things, but haven't had many dealings with eigenvectors. So that information was genuinely new to me. My expression of gratitude was sincere.
- srean 8mo ago
  Understood and thanks for the opportunity of sharing together in the joy of something so amusing.
riffic 8mo ago
You're doing this multiple times, but it's can only mean "It Is" or "It Has".
- srean 8mo ago
  Thanks for the heads up. I meant 'its'. Phone autocorrect always interferes and I get tired and lazy about correcting it back. It does get it right most of the time.

by srean 8mo ago

Sharlin 8mo ago

Their point was that "familiarity" apparently means different things for different people :P Someone using linalg in computer graphics applications may say they're familiar with it even though they've never heard the term "eigenvector". I'm not actually sure about what you mean – how does repeated multiplication reveal eigenvectors?

srean 8mo ago
Consider a diagonalizable matrix A. For example, a real symmetric matrix. Start with any vector b and keep multiplying it with A. A A A ... A b The vector that the result will converge to is a scaled version of one of the eigenvectors of the matrix A. But which one ? The one with the largest eigenvalue among all eigenvectors not orthogonal to b. https://en.wikipedia.org/wiki/Power_iteration https://en.wikipedia.org/wiki/Power_iteration
- Sharlin 8mo ago
  Ah… that "diagonalizable" is doing some heavy lifting there! I was wondering how exactly you’re going to make, say, a rotation matrix to converge anything to anything that’s not already an eigenvector. And rotation matrices certainly aren’t degenerate! Though apparently non-diagonalizable matrices can be called defective which is such a dismissive term :( Poor rotation matrices, why are they dissed so?!
  - srean 8mo ago
    Love them, those rotation matrices. Take logarithm of the eigenvalues and you get back the angle. This to me had solidified the notion that angles are essentially a logarithmic notion ... Made more rigorous by the notion of exponential maps

CoastalCoder 8mo ago

My first sentence was in jest. I've used LA for various things, but haven't had many dealings with eigenvectors. So that information was genuinely new to me. My expression of gratitude was sincere.

srean 8mo ago
Understood and thanks for the opportunity of sharing together in the joy of something so amusing.

riffic 8mo ago

You're doing this multiple times, but it's can only mean "It Is" or "It Has".

srean 8mo ago
Thanks for the heads up. I meant 'its'. Phone autocorrect always interferes and I get tired and lazy about correcting it back. It does get it right most of the time.