## Problem with QR algorithm...

I'm trying to implement the QR algorithm to find the Eigenvalues of the input matrix which will be forwarded to another implementation (of the SVD alg.) to find the singular values. My implementation goes as follows:

1. feeding input: A::Matrix(datatype=float) # a bidiagonal matrix
2. construct input matrix for the QR alg. of matrix A and Z (zeros of size A): C := Matrix([[Z,Transpose(A)],[A,Z]], datatype=float); # therefore C should be symmetric
3. find the eigenvalues of matrix C with an implementation of the QR alg.:

for k from 1 to 400 do
Q, R := QRDecomposition(C);
C:=R.Q;
end do:

At this point, the eigenvalues of C should be placed in the diagonal of the matrix, but they're randomly placed around the diagonal, with only ~0 elements (like 2,xxx * 10^(-13)) in the diagonal.

If anyone knows how to resolve this, let the knowledge flow through. Any help will be appriciated, thanks in advance.

## plotting faster intensity levels in an image...

Is there another way to plot 3d intensity levels in an image?  Using matrixplot takes a long time.

restart;gc():
with(ImageTools):
with(plots):

b:=convert(ToGrayscale(a),Array):
c:=convert(b,Matrix):

## Error in LA_Main:-SingularValues...

with(LinearAlgebra);
CAb := <1, 1, 2;1, 2, 3;1, 3, 1>;
# Get the QR decomposition of CAb:
Q, R := QRDecomposition(CAb); R;

Error in R

Maple Matrix(3, 3, {(1, 1) = 1.7321, (1, 2) = 3.4642, (1, 3) = 3.4642, (2, 1) = 0., (2, 2) = 1.4142, (2, 3) = -.70710, (3, 1) = 0., (3, 2) = 0., (3, 3) = 1.2248})

MathCad Matrix(3, 3, {(1, 1) = 1.7321, (1, 2) = 3.4642, (1, 3) = 3.4642, (2, 1) = 0., (2, 2) = 1.4142, (2, 3) =...

## Error, (in Statistics:-Fit) SVD of estimated Jacob...

I am trying to fit some data to a model.

The model is given by this equation.

A*(C/B)^(2*B)*(B-1)^(2*(B-1))/(205*10^9*(2*B+1)*(sigma^2-(650*10^6)^2)*sigma^(2*(B-1)))+(C-sigma)^2*A/(205*10^9*(2*B+1)*(sigma^2-(650*10^6)^2))

> with(Statistics);
> X := Vector([819.4, 795.6, 788.8, 782.0, 776.56, 763.64, 748.28, 724.42, 717.40, 711.28, 707.20, 680], datatype = float);
> Y := Vector([5.3*10^4, 7.8*10^4, 9*10^4, 9.5*10^4, 10^5, 1.2*10^5, 1.37*10^5,...

## 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

## Algorithm used for singular value decomposition i...

Which algorithm does maple follow for singular value decomposition by command 'SingularValues' in LinearAlgebra Package ?  Is it is QRSVD or divide and conquer or any other   .As far as  I know, MATLAB uses QRSVD.

## Jacobi SVD function...

Hi,

Is there any  function  in maple to compute the SVD of a matrix  using jacobi method? Or anybody has maple code to do so?

## setoptions3d vs ApplyLinearTransformPlot function....

Visualizing_the_SVD_.mw

Hola ev1:

I like to shorten the size of the command, through setoptions3d function. But it seems that it does not interact with ApplyLinearTransformPlot function.
How to get to label the vectors?

Gracias

## Curve Fitting and SVD...

First of all my apologies for having improperly inserted graphic. As you can see in the document, Application 2, the graph is the result of having made an adjustment using SVD. I have tried to repeat the adjustment with Maple and this is what I get. Anything. Where is the problem. Any help?

## CANDECOMP/PARAFAC: images as tensors of order 3

by: Maple 14

This post is a further development of my earlier question in reply to John's post. I have implemented a basic version of the CANDECOMP/PARAFAC algorithm referred to on Wikipedia and described

## Decompose a third order tensor into pure tensors?...

If you construct the tensor product W of an m- and an n-dimensional vector space, U and V, then you can view the elements of W as m by n matrices (by picking a basis for U and V). The rank one matrices are the elements that can be written as the tensor product of (nonzero) vectors u in U and v in V; this corresponds to writing the matrix as u

## Unleashing Your Rank Four Self

by: Maple 14

I have gotten some comments about my new avatar, including a few commenting that while my picture is clear on the blog contributors sidebar, it is "blurry" on my blog posts. I just wanted clear this up.  I am not in the witness protection program; I just really love singular values.  My new avatar, just like my old one, is a rank 4 approximation of a picture of me using the singular value decomposition.

## LinearAlgebra vs linalg...

`What is the Problem? Do not use SingularValues (A, output = ['list'])?Some care in handling this command?`

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