Linear Algebra 20k: Two Derivations of the Dot Product Component Space Expression

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  1. MathTheBeautiful
  2. Pavel Grinfeld
  3. Linear Combinations
  4. Eigenvalues
  5. Gaussian Elimination
  6. Determinant
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Комментарии
Автор

Superb course! wow! It helps me a lot that this LA course starts with 2d and 3d geometry to build a solid foundation.

martin
Автор

Thank you for directing me to this lecture! I can see that they are indeed beautiful proofs, especially the second one. Wow!..

albertlee
Автор

Hi sir, I've a fundamental question at this point. What does it mean to dot two vectors? How should I think about the intuition?

PraveenKumar-exiw
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why is the 2nd proof generally applicable when it relied on orthonormal basis vectors?

HushMoney
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+MathTheBeautiful You make a huge assumption in the second proof while foiling the stuff inside the parentheses - that alpha1e1 *dot* beta1e1 is the same as alpha1beta1(e1 *dot* e1) for the first two terms, and so on. In other words, you are *mixing multiplication and dotting operations* - how can you do this and just assume it works? I don't believe we have covered this mixing of operations and if so, could you please explain? Thanks.

tangolasher