Recent content by prhzn

Anyone who knows the limits of orthogonality for Bessel polynomials? Been searching the Internet for a while now and I can't find a single source which explicitly states these limits (wiki, wolfram, articles, etc). One thought: since the Bessel polynomials can be expressed as a generalized...

Hm, I'm not sure if I get this 100%. How should I express/extend the \mathbf{T}' matrix before trying to diagonalize it? I also see know that I should have posted this in the Linear & Abstract algebra forum instead, as this isn't a homework/text-book question ;)

I see that my formulation became a bit unclear. Your alternative representation is indeed better - didn't think of that. However, even from \mathbf{P}\mathbf{A}=\mathbf{W}\mathbf{T}\mathbf{P}\mathbf{W} I will still end up with expressions that are quite similar to the original expression. I.e...

I have the equation \mathbf{A}=\mathbf{W}_1\mathbf{T}\mathbf{W}_2 that represent some measurement setup I have at the uni. lab. The matrices are given as \mathbf{A}= \begin{bmatrix}a1 & a2\\a2 & a1\end{bmatrix}\,\mathbf{W}_1=\begin{bmatrix}w_{11} & w_{12}\\w_{21} &...

Figured it out - used the definition of the singular values of A, and then prooved that the singular values of ATA are the squared singular values of A.

Homework Statement Prove that \kappa(A^TA) = \kappa(A)^2 where \kappa(A) = \left\|A\right\|\left\|A^{-1}\right\|, or in a more general case, \kappa(A) = \left\|A\right\|\left\|A^+\right\|, where A^+ is the pseudoinverse of A\in\mathbb{R}^{m\times n} The Attempt at a Solution My initial guess...

Not sure if this is correct, maybe someone can tell or not? We know that \mathbf{\theta}[n] = \mathbf{A}\mathbf{\theta}[n-1] for n\geq 1. Then \mathbf{\theta}[n] = \mathbf{A}\left(\mathbf{A}\mathbf{\theta}[n-2]\right) and so on, resulting in \mathbf{\theta}[n] = \mathbf{A}^n\mathbf{\theta}[0]...

Homework Statement Consider a parameter \mathbf{\theta} which changes with time according to the deterministic relation \mathbf{\theta}\left[n\right] = \mathbf{A}\mathbf{\theta}\left[n-1\right]\; n\geq 1, where \mathbf{A} is a known p\times p matrix and \mathbf{\theta}\left[0\right] is an...