Recent content by JohnLang

OK I'll give it a shot. I did give up on the problem because it seemed really annoying

btw each of the non zero eigenvalues have a corresponding eigenvector because geometric multiplicity is always less than or equal to algebraic multiplicity right?

Hmm, this is interesting, since T has 2 distinct eigenvalues in which I'll presume, furthermore since the other eigenvalues are all zero, is this enough to say that T is diagonalizable? Would that help in me in analyzing how T maps R?

haha thanks for all the help!

is it fair to say that only the first 2 rows of T will be considered in the general case of finding the 2x2 principal submatricies since the rank of T is 2 meaning there are a lot of zero rows?

WOOT! ok the 4x4 case worked, let's see if I can get it going for the general case, at least I know there are n choose 2 principal 2x2 minors

sorry 34, also if I'm going to calculate the principal minors for 2x2 that means there will be 6 of them for the 4x4 case right? 4 choose 2?

so when I do it this way I get the characteristic polynomial, p(λ)=-λ(λ2-15λ-18) and that gives me the correct eigenvalues the principal minors are [5 6;8 9] [1 3;7 9] [1 2;4 5] the sum of the principal minors give me -18, furthermore I see that the trace is b. but when I do...

I'm having problems when I'm calculating 4x4 matricies, my principal 3x3 minors are all 0 which makes sense since the rank of A is 2 so in this case rref(A) will have 2 rows of zeros which implies the determinant of A is 0. Any further suggestions?

Robert: So when I row reduced this matrix it looks something like this [1 0 -1 -2 -3 ... 1-n;0 1 2 3 4 5 ... n-1;(remaining rows are 0) which means that this matrix has rank 2 from here what should I do? Also since the matrix T has rank 2, this means that there are non zero principal (2x2)...

Hi, I Like Serena! Thanks for welcoming me! Anyway, so far I think I was able to show that the rank of the matrix which is 2 I used a really rough method so I think what this means for the characteristic polynomial, it's going to look something like this p(t)=tn-2(t2-bt+c) I'm kinda stuck...

I feel like I need to exploit some properties of determinants.

Homework Statement Let T be a square nxn matrix and let each entry tij=n(i-1)+j. Calculate the eigenvalues of T of T when T is a 3x3 matrix and a 4x4 matrix. Homework Equations The Attempt at a Solution For the homework I'm supposed to calculate the 3x3 case and the 4x4 case. Then it says...