Linear Algebra 18b: A Worked out Eigenvalue Decomposition Example

[@MathTheBeautiful]

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[@aschwarzinger1967]

These videos have help me understand linear algebra more than any other material I have seen yet. I'm happy to support it.

[@izzyhargrave6370]

This man is excellent at explaining math

[@shreejanshrestha1931]

LoL because of that guitarist I was so distracted that I was scratching my head thinking which technique is this to find an inverse. Later realized it was augmentation and RREF.

[@MathTheBeautiful]

I'm sorry, I didn't follow the question - I was listening to the guitarist.

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Great song

[@scitwi9164]

So how does it map to finding eigenvalues and eigenfunctins of *differential operators* instead of matrices?

[@NotLegato]

there is not really any general way for finding eigenvalues for infinite-dimensional linear operators. however, if we're just talking about differentiation, you'll see that all elements ce^(ax) are eigenvectors with eigenvalue a, and constant functions are eigenvectors with eigenvalue 0, and so on. as an additional curiosity, if you choose a polynomial basis (1 , x , x^2/2 , x^3/6 , x^4/24 , ...), then you'll see that the derivative maps each basis vector to the next one in the sequence.

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twoset needs to react to this

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like th video like the song thank you