Recent content by brru25

Homework Statement Find the solution to the two-point boundary value problem u'' + 4u' + exu = sin(8x) with u(-1) = u(1) = 0. Homework Equations The Attempt at a Solution I haven't taken an ODE course in years but I need to verify that my numerical solution to the ODE is accurate to the...

Homework Statement Show that the integral from -1 to 1 of p(x)*log|z-x| dx equals log|z - sqrt(z^2 -1)| / 2, where p(x) = 1 / (pi*sqrt(1-x^2)) 2. Other information This topic comes from Chebyshev interpolation. p(x) is the Chebyshev density. The Attempt at a Solution The best idea I could...

positive, word-for-word...see why I'm confused? :-)

it's multiplication not conjugate (sorry about the mix-up everybody!)

Homework Statement Let A be an n×n real matrix. Show that there exists S such that SAS-1 is block upper triangular with diagonal blocks of size at most 2. Homework Equations BUP = block upper triangular The Attempt at a Solution It sounds a lot like the Schur decomposition (which...

Homework Statement Let U be a vector subspace of C2n such that sum(xi*yi) = 0 for 1 <= i <= 2n for any x, y ∈ U. Show that dim U <= n. Give an example of such a subspace U with dim U = n 2. The attempt at a solution I tried just writing out the summation and was thinking along the lines of...

Yea I assumed by accident it was linear. Yea I understand that there are only p values in Fp but I don't know how to make the connection to a polynomial. I mean I know a polynomial of degree p-1 has p coefficients but for some reason I can't connect the dots.

Would polynomial interpolation work here?

1. The problem statement For integers m >= n, Prove det(xIm - AB) = xm-ndet(xIn - BA) for any x in R. Homework Equations A is an m x n matrix B is an n x m matrix The Attempt at a Solution I tried working out the characteristic polynomials by hand but it just seems too tedious...

Yea you're right. We were just trying to think of different approaches to the problem.

I agree completely. For now I can use the |P-1| = 1/|P|. Concept. A second opinion basically said the same things we were saying so that will have to be my route. Thank you for your help.

Only problem is a determinant is being used in the proof which isn't allowed.

Well I was thinking on the lines of rank-nullity theorem but I didn't see how that would apply here. I was also thinking of assuming each A_i was a matrix of entirely zero except for one row (or column), of which has only one entry of 1...e.g. |0 0 0 0| |0 0 0 0| |1 0 0 0| |0 0 0 0| Each A_i...

Yea I was thinking the same thing about showing they have the same determinant, because I would think that would be enough.

Is it possible for m = n+1 if there exists u1, ..., um in Rn such that the distance between ui and uj is 1 for any 1 <= i < j <= n?