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Chebyshev polynomials have the form:

Tn(x) = cos(n*arccos(x))

orthogonality interval is (-1, 1) for n = (2, 3, 4,

1. I use your previous reply on V_G derive  on other characteristic function, but most are undefined

or complicated solution or can not evaluate, why?

for example

charc := 1+i*X/(i*X-1);
int(exp(-I*X*u)*charc, X = -infinity .. infinity);

it got this complicated thing
piecewise(Im(1/i) = 0, undefined, int(exp(-I*X*u)*(1+i*X/(i*X-1)), X = -infinity .. infinity, method = _UNEVAL))

Density := int(exp(-I*X*u)*charc, X = -infinity .. infinity);

Hi guys, I would like some help writing a procedure that checks whether the group of input vectors is an orthogonal basis. Any help would be great!

Sorry, this seems like a silly question. But is there an easy way to convert trig funcitons, or even non trig functions to orthogonal (in this case Legendre) polynomials? 

How can I show that the Least Square solution x = (A'.A)^-1.A'.y
Is different when A is an orthogonal matrix compared to an
overdetermined or underdetermind matrix.

Preferably transform the matrix using Singular Value Decomposition (SVD)
or something similar.

Thanx

Help!

I've used Eigenvectors to solve for eigenvalues & eigenvectors.  Eigenvalues works, no problem.

The eigenvectors are not normalized to unit magnitude (how would I do that for all eigenvectors?) and the usual matrix multiplication of the eigenmatrix by its transpose should give the identity matrix--and somehow it does not. 

Can someone point out the flaw in my thinking?  The file is attached.

Thanks for you insight!