Unable to calculate the Determinant of a large matrix

[Avodyne]

I'm not sure what Hurkyl had in mind, but you can get the multiplicities by noting that Tr A = n. (I had this in my original post, but then edited it out so as not to be giving out too much info to the OP.)

 

[Dick]

I'm not sure what Hurkyl had in mind, but you can get the multiplicities by noting that Tr A = n. (I had this in my original post, but then edited it out so as not to be giving out too much info to the OP.)

Oh, yeah. That works. Thanks!

 

[Count Iblis]

Problem solved, it is time to http://arxiv.org/abs/math/9902004"

 

[Dick]

Why? This ones been solved at least two ways. I'm sure there's a million other ways. I'm still kind of leaning to the row reduction as the simplest.

 

[Hurkyl]

I can see how that will get you a minimal polynomial, but I don't see how to get to the characteristic polynomial. How do you count the multiplicities?

A is diagonalizable, and we know its rank.

 

[conway]

Problem solved, it is time to http://arxiv.org/abs/math/9902004"

Well, there's one last point that I'm wondering about: where does this problem come from? Is it just a math question or does it relate to some actual physics or anything else?

 

[soopo]

I'm not sure what Hurkyl had in mind, but you can get the multiplicities by noting that Tr A = n. (I had this in my original post, but then edited it out so as not to be giving out too much info to the OP.)

What is the Tr A = n?
Do you mean transpose of A equals to n that is the size of the matrix?

 

[Count Iblis]

What is the Tr A = n?
Do you mean transpose of A equals to n that is the size of the matrix?

"Tr" means the "trace", i.e. the sum of all the diagonal elements. This is invariant under a change of basis:

Tr[A] = sum over i of A_{i,i}


Tr[S^(-1)AS] =(ommitting summation signs, we are summing over all epeated indices) =

S^(-1)_{i,k}A_{k,j}S_{j,i}= Tr[***^(-1)] = Tr[A]

 

[soopo]

"Tr" means the "trace", i.e. the sum of all the diagonal elements. This is invariant under a change of basis:

Tr[A] = sum over i of A_{i,i}


Tr[S^(-1)AS] =(ommitting summation signs, we are summing over all epeated indices) =

S^(-1)_{i,k}A_{k,j}S_{j,i}= Tr[***^(-1)] = Tr[A]

How can you solve the problem by using trace?
I cannot see how you can proceed with them.