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 definiton 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...
Homework Statement
Transform to normal form and solve:
1) u_{xx}+u_{xy}-2u_{yy} = 0Homework Equations
Normal form: Au_{xx}+2Bu_{xy}+Cu_{yy}, hence, A = 1, B = \frac{1}{2}, C = -2.
Since AC-B^2 = -2.25 < 0 this is a hyperbolic equation.
Want to transform it by setting
v = \Phi(x,y), z =...
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...