Example of Invariant Subspace

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Matrix Theory: Let T: R^4 to R^4 be the linear transformation that sends v to Av where A = [0 0 0 -1 \ 1 0 0 0 \ 0 1 0 -2 \ 0 0 1 0]. Find all subspaces invariant under T.

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Very clear as always. Not even an extraneous word. Really helpful!

Leperkahn

You are amazing, finally, I understood that!!! Please don't stop making videos.

mariagonzalez-pdor

Nick cage got really buff and started teaching linear algebra... it's Ghost Rider 3, coming to a theatre near you...

tripp

This guy teaches math like a football coach giving a motivational speech.

nicholassimafranca

Thank you for making these videos. You have a good pedagogical style. Unlike the overwhelming majority of these types of lectures, you take a brief pause after each clause which may require a moment of reflection to understand. This is great! People will often just charge from one statement to another, never giving the audience time to digest. Ofc on youtube you can just pause, haha but during in person lectures, it can really hurt students understanding

workerpowernow

@candamohcine My background is in Lie groups, so matrices are definitely where I live. - Bob

MathDoctorBob

It was planned, but never shot. Same problem, but with C^4.

MathDoctorBob

If you don't have any 1-dim invariant subspaces (aka eigenspaces) doesn't this actually imply that you cannot ever have any n-1 dimensional ivariants? Since you need to be able to decompose the entire image of a transformation into a direct sum of invariants the step seems a little redundant

cmdstraker

I have a very basic question. For a subspace with dimension 3. We have 3 vectors in R^4. if M is 3 x 3, Mv wouldn't be feasible due to dimension mismatch . What am I missing?

ritupande

When would the non-empty intersection of two planes not have dimension greater than zero? I'm not sure demonstrating uniqueness of the two dimensional subspace was necessary, as the intersection can't be empty, {0}, or a line.

jennysmith

Is there a video called "Example of Invariant Subspace 2" that I'm missing?

cmdstraker

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