Recent content by Alupsaiu

Hey, thanks for the reply. I figured the problem out a while ago, I don't know exactly why I found it confusing, long day I suppose haha. Thanks for the help though!

To be more specific, the problem is to show for any integer n≥2

Hi, I'm working a problem and I'm stuck on one part. Consider, X and Y, two independent discrete random variables who have the same geometric pmf. Show that for all n ≥ 2, the PMF P(X=k|X+Y=n) is uniform. Now, this equals: P(X=k)P(Y=n-k)/P(X+Y=n), which follows from the definition of...

Man I hate how painfully simple problems like these are when you see them done haha...thanks a bunch

If v is in Rn and is an eigenvector of matrix A, and P is an invertible matrix, how would you go about finding an eigenvector w of PAP-1? I'm thinking you have to use a fact about similarity?

I found a fact on wikipedia saying that any square matrix has a Jordan normal form if the field of coefficients is extended to one containing all the eigenvalues of the matrix. How would you go about showing this?

Ok, so it was easy to show linear independence, then I found the matrix which had in the first column the coordinates of Nv, and in the second column 0 since N^2=0. So, x1 0 x2 0, where x1 and x2 are the coordinates of Nv in basis (v, Nv). Would x1 actually turn out to be 0? But...

The wording is from a problem I found online, but I think similarity is what they're after. I'm not sure what else it could mean. Thanks for the help. Now time to google Jordan normal form.

Hi, Is every matrix similar to a triangular matrix? If it is, anyone have an idea how to prove it? Thanks

Homework Statement Prove any nxn matrix can be written as in block form N 0 0 B where N is a kxk nilpotent matrix and B is an (n-k)x(n-k) invertible matrix. Need help getting started, or any hints/any help at all would be really appreciated. Thank you!

Suppose N is a 2x2 complex matrix such that N^2=0. Prove that either N=0 or N is similar over C to the matrix 00 10Sorry, I don't know how else to write the matrix in the post. Any help would be greatly appreciated, thank you.

...Moments like these I feel so small...haha thanks a bunch

I'm having trouble showing that any normal linear transformation T is the sum of a self-adjoint transformation T1 and anti-self adjoint linear transformation T2, (so T=T1+T2) so that T1 and T2 commute. Anti-self adjoint being <Ta,b>=-<a,Tb>. Specifically I'm not sure how to use the information...