Not diagonalizable

Example of non-diagonalizable matrix. Exact conditions for a matrix to be (or not to be) diagonalizable. Algebraic and geometric multiplicity of an eigenvalue

[yevonnaelandrew]

"Whoo. Fancy". I like the expression a lot! You have a very nice personality, Dr. Peyam! :D

[cameronspalding]

In order for a matrix to be diagnosable the algebraic multiplicities must match the geometric multiplicities

[isaackay]

Gosh I love my Applied Math prof/advisor and his lectures, but it's a real treat to watch your videos

[PunmasterSTP]

Not diagonalizable? More like "Note well, this information is incredible!" Thanks for making and sharing so many illuminating videos.

[leonardopereira]

I am from Brazil and, I didn't find any video about not diagonalizable matrix, so thank you.

[carterwoodson]

Just came here from the diagonalizable matrix video because I had this exact matrix in mind! haha

Thank you very much Dr. Peyam!

I noticed however that the n-th power of this matrix looks like {[1, n], [0, 1]} That is interesting!

It would mean that the product of two matrices of this form is still of this form, so it's closed

The are also all invertible, and commutative, the identity is in there as well.

so they would form a group! but I dont know if I should be able to extend that property to say the rational numbers.

[seeforkat]

Algebraic multiplicity of a certain eigenvalue λ is basically the number of eigenspaces that is scaled by this particular λ.
Geometric multiplicity is actual number of eigenspaces.

[ClumpypooCP]

Who else is in a linear algebra class this semester?

[georgesadler]

Thank you for the video. I am still learning about this topic.

[brianlamptey]

So why is the identity matrix diagonalizable? Is it because there is only one eigenvalue and one eigenvector?

[dream]

If we can’t find the eigenvalues of the given matrix or characteristic polynomial have no solution, it means that, is matrix not diagonalizable??

[chloewho]

Didn't you go to Berkeley? I think I remember watching my roommate watch some videos of you once. You were like a GSI for some class but i forgot. Anyways thanks for this video! very helpful for ee16b lol.

[letsknowfromscratch]

Hello sir, but why [1101] is not diagonalizable

[pinoyguitartv]

Hi sir,
How can I convert a non diagonally dominant matrix into one, ?

I'm to apply the Gauss Jacobi and Gauss seidel method requiring that,


What if rearranging terms don't work?,

Great discussion btw!!!
👍👍👍💯

[svanalakshmis]

Matrix [0 1:10] is diagonalizable or not sir

[yxlxfxf]

Would be nice to follow this with a video on Jordan forms!

[MrRyanroberson]

Is it possible for an nxn matrix to have more than n eigenvectors? i'm guessing no, but i wonder if it's possible to have multiple unique pdp^-1 situations

[Nockoutz]

Thank you very much, helped me a lot!

[brianlamptey]

How would you define algebraic multiplicity? As the order of the determinant?
Although I do understand that geometric multiplicity is the number of eigenvectors.

[jamesa.]

Dude thank you so much I was so stuck, on this. Your video really helped alot