## Orthogonal, rotational matrices...

I've got the following matrix :

A:=[<a,a-1,-b>|<a-1,a,-b>,<b,b,2a-1>] where <> are the column elements of A, a is  a real number defined on [0,1] and b^2=2a(1-a)

a) to show A is an orthogonal matrix, I understand that I need A.Transpose(A)=Identity(3*3) but is there a way in which I can let a take a random real numbered value between 0 and 1? The rand() only returns an integer within a range. Directly multiplying A and Transpose(A) will return an expression in a, so what's the right approach?

b) from a) we can infer that A is a matrix that describes a rotation in e1,e2,e3 where these are the standard bases vectors in R3. How can I determine the rotation axis? The hint I've been given says I need to consider the Eigenvalues and eigen vectors but I don't quite understand how.

## Simplifications of Expressions containing Orthogon...

I am trying to simplify sums of a few LaguerreL polinomials of different n using the identities in the function advisor such as recurrsion relations. How does one go about in using the FunctionAdvisor identities when trying to simplify expressions containing orthogonal polynomials?

## Hybrid function...

Hi all.

In the following program, i have normalized bernstein polynomials using gram- schmidt orthogonalization process and want to hybrid them with block pulse functions so that i have:

why the program is wrong?? where of it doesn't work properly?

best wishes

OHB.mws

Ph.D Candidate

Applied Mathematics Department

## Hybrid of bernstein and block pulse...

Hi all

Assume that we have construct new orthogonal Hybrid function of block pulse and bernstein poly nomials as follow:

and assume that we want to approximate a function as follows:

how can we do this with maple????Indeed we want to optimize using this hybrid functions

note that the degree of bernstein polynomials is fix or should be fixed...and

regards

Ph.D Candidate

Applied Mathematics Department

## How to do Gram-Schmidt orthogonal in Maple?...

computer the Gram-Schmidt orthogonal of (22,11,5),(13,6,3),(-5,-2,-1) belong to R^3.

## Recursion in FourierSeries (OrthgonalExpansions)...

So I am working with the OrthgonalExpansions library (amazing library, by the way! Just what I needed!), and it is great, except it seems to be having trouble doing a 2d Fourier expansion.

In this document, I am running the BesselSeries expansion as we speak, but the FourierSeries expansion (in 2d) can never seem to complete. It always say that it has an

## Chebyshev polynomial to write a program...

Chebyshev polynomials have the form:

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

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

## How to integrate this case...

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);

## how to check if a group of vectors is an orthogona...

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!

## LS, SVD and Orthogonal Matrix...

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

## shouldn't eigenvectors be normalized?...

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!

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