Lec 24b | MIT 18.06 Linear Algebra, Spring 2005

[kotofu]

Finals. Only one left and it's Christmas.

[akhil089]

thanks professor gilbert

[zkhandwala]

I may have missed it in the previous lectures, but can someone remind me why the eigenvalues of the inverse of A are simply the reciprocals of the eigenvalues of A?

[yuppygoat]

@zkhandwala

(A' represents A inverse)

AX=λX

A'AX=A'(λX)

IX=λ(A'X)

(1/λ)X=(A'X)

A'X=(1/λ)X

That last equation is just like the first, it's an eigenvector-equation. The eigenvalue is now (1/λ). This only holds if A is invertable, of course.

[jae44]

This guy is wayyyyyyyyyyyyyyyy better then my Linear Algebra professor. In the first 5 minutes I've learned more then I did all semester.

[DBangaDon]

These lectures are great and I really respect MIT for doing this, much more so than other high level universities, but shit, man. How hard is it to make a video of a dude talking at a blackboard? It would probably take less than 5 minutes to put a little bit of gain on the audio file and for over 5,000 views I'd say those 5 minutes would be well spent.