Setting up eigenvalue in mathcad

[JBlackhole]

to all

I am struggling to set up the eigenvalue described in the attached mcad v15 sheet (or pdf). Could someone who understand these things enlighten me?

Thanks

Regards

[AlanStevens]

Is something like the attached what you are looking for?

Alan

[JBlackhole]

Thanks for the input. Appreciated. Looks like I do not quite fully understand the equation (yet) as if one plots the results of the eigenvalue extraction the result is not what I expected. I attached a typical example of such plot

[-MFra-]

Hi,

The matrices A and B are singular, so it is not possible to calculate the eigenvalues.

[JBlackhole]

Thanks. Is it my test vector which is not correct? (does not work with 1 vector !) Do I need more vectors to make it work?

[-MFra-]

You must make sure that | A | and of | B |, be different from zero. As you can see, in my calculations, I haven't multiplied by the matrix M when creating the matrices A and B. Mathcad defines an array as column vector and, consequently, the transpose is a row vector. It follows that HTMH is a scalar, and the eigenvalues equation looses meaning. You should reconsider the whole theory and how the text book defines the array (column or row?).

[JBlackhole]

Thanks for that. The theory part is pasted in the originally posted mcad sheet. I suspect that where [Hr(w)] is specified it's a matrix and I set-up my test with a vector ! One member corrected xv to XV from my original post to make it a matrix to make it work. I still don't know what sort of result to expect.

[-MFra-]

Hi,

I would like to remind you that the algebra of matrices is a non-commutative algebra (A*B≠B*A) and in which only the operations of sum, subtraction, multiplication and inversion are defined (the division between matrices is not defined). You provide only the vector xv, there is no way to continue. In the text you provide, H is defined as a complex (No * Ni) matrix, and nothing else.