Differential Equations | Matrix Exponential Example: Diagonalizable Case

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We present the general form for the matrix exponential of a diagonalizable matrix and a corresponding example.

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There is a computing error in the example. The null spaces (eigenvectors) are swapped. E.g. at 7:45 the board shows the computed eigenvectors. That's the right moment to check the eigenvectors on the original matrix A.

For the rest your channel is awesome. Advanced interesting math is explained thoroughly!

petervandenheuvel

Guys whoever looking to these videos must share this channel to their friend circle bcoz Mr.penn is really a good guy....I wish his channel grow by f(x)=e^x

hustler

So, by the same logic we generalize any function which can be expressed as a power series when applied to diagonalizable matrices. (Sine and cosine are obvious examples). But is it helpful to also generalize all functions when applied to a diagonalizable matrix this way? Even when they cannot be expressed as a power series?

Nathan

plz tell me about your research “Principal Subspaces of Twisted Modules for Certain Lattice Vertex Operator Algebras” i cant understand

Ravit

It seems like there is nothing special about exponentials here and it would work with most functions?

binaryblade

at which rule you write the exponential only in the middle and leave the left and right matrix p and inverse of p

ibrarkhan

Do these relate to the generators of groups.

aidansgarlato

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