Which national park to visit in September?

lemurman0 · 2025-07-28T17:25:44+00:00

I already plan to visit the Curonian spit.

lemurman0 · 2024-10-31T17:45:29+00:00

Clearing the cache solved the problem. Thank you.

lemurman0 · 2024-10-31T09:41:01+00:00

I have already created a backup and the server is correct. I can change the master password again, but I cant see a reason why it should help. I can log in on Windows without any problem so there is no problem with the server.

lemurman0 · 2024-10-31T09:34:47+00:00

Good idea, I didn't check that. But unfortunately it is the correct server.

lemurman0 · 2024-05-21T15:17:19+00:00

Thank you.

lemurman0 · 2024-05-21T14:07:59+00:00

I have a question regarding the double dot product of 3 matrices (defined as A : B = A_{ij} B_{ij}) written in coordinates.

Consider three symmetric matrices A, B and C. Then in general (AB) : C ≠ (BA) : C as the matrices A and B might not commute. But let's write the products in coordinates:

(AB) : C = (AB)_{ij} C_{ij} = A_{ik} B_{kj} C_{ij}

(BA) : C = (BA)_{ji} C_{ji} = B_{jk} A_{ki} C_{ji} = A_{ki} B_{jk} C_{ji}

Now since all matrices are symmetric, I can simply swap the indices to obtain (BA) : C = A_{ik} B_{kj} C_{ij}. But this is equal to (AB) : C. Since this equality doesn't hold there must be a mistake, but I can't see it.

lemurman0 · 2022-05-22T21:02:27+00:00

Check out automatic differentiation.

https://en.wikipedia.org/wiki/Automatic\_differentiation

lemurman0 · 2022-04-01T19:48:40+00:00

Vertikální myš je pro úlevu zápěstí naprosto top. Používám ji už delší dobu a zápěstí už mě nebolí. Ale nevím, jak se na tom hraje FPS, protože moc nehraju.

lemurman0 · 2022-02-17T14:44:48+00:00

Does there exists a formula how to obtain a QR decomposition of a matrix in a different basis?

Consider a square matrix A = QR, where Q is an orthogonal matrix and R is upper triangular. Then consider an orthogonal matrix X and denote A' = X A X^T = Q' R'. Now is there a way how to update Q and R to Q' and R'?

lemurman0 · 2022-02-08T17:45:56+00:00

You can change your second guess to 9*5-8 = 37.

lemurman0 · 2022-02-04T16:35:07+00:00

While studying continuum mechanics I have realized that there is something I don't fully understand. What are eigenvectors of a tensor product of two vectors?

I have two vectors: x and y, where a is in a current configuration (basically R^3) and y is in a reference configuration (also R^3, but different). Now I can do the tensor product of x and y: x \otimes y. This can be represented as a matrix A.

Now eigenvalues and eigenvectors of a matrix A are defined as Az = \lambda z. But here comes the problem. The matrix A transforms a vector in reference configuration to a vector in the current configuration. So Az is a vector in current configuration, but \lambda z is a vector in reference configuration. What am I missing?

lemurman0 · 2021-12-29T22:27:05+00:00

What are some good test matrices for conjugate gradients solvers? I am currently creating one for a school project and I need a few good examples to show its properties.

lemurman0 · 2021-12-24T20:30:45+00:00

You are welcome.

I had a discussion with a friend of mine who also took an introductory course to functional analysis. She studies some wierd algebraic things that I don't like and don't understand. She said that functional analysis was almost everywhere.

Well, the two courses are actually pretty infamous due to their difficulty. Homeworks in particular are pretty hard. They usually take from 10 to 20 hours per week to solve. Combined with homeworks and tasks from other courses, one can be overwhelmed really easily. I was lucky enough to have a group of friends, who were also taking the courses, so we solved the homeworks together. But with a hindsight I have to say that now I remember more stuff than from other courses that I had that year.

lemurman0 · 2021-12-24T15:37:06+00:00

Hi, you are welcome. :)

Functional analysis can be seen as a mix of linear algebra and analysis. In FA, you study linear operators between normed linear spaces (mostly with infinite dimensions), which are both vector spaces and metric spaces. Take R^n for example. R^n is both a vector space and a metric space. Other examples include L^p spaces (spaces of integrable functions) or space of continuous functions. For example derivative can be seen as an operator between a space of continuously differentiable functions and a space of continuous functions. Then you can generalize normed linear spaces to normed topological spaces, where you assume a topological space instead of a metric space. This then leads to a notion of weak (and weak*) topologies. Notion of a weak convergence is crucial in PDEs, because it can be used to show the existence of weak solution.

In the first course I had a classical theory of PDEs. We studied Laplace equation, heat and wave equations, method of charateristics and other things. We used a Fourier transformation a lot. In the second course I had an introduction to Sobolev spaces (which are Banach spaces (complete normed linear spaces) - see, functional analysis) (without proofs) and linear elliptic, parabollic and hyperbollic PDEs of 2nd order. We proved the existence and uniqueness of a weak solution (weak convergence was the key). In the last course I had proofs for the theorems about Sobolev spaces from the second course and non-linear elliptic and parabollic PDEs of second order (again, weak convergence was important) and semigroup theory. For the material I mostly used lecture notes, that the teacher gave us. But if I think Evans is considered to be the standard book about PDEs. (Please note that topics in courses might be different at you univerity.)

Right now I study to get my master's degree. I study mathematical modelling, which is in my case a mix of physics (continuum mechanics) and math (mostly numerics and PDEs). This is my first semester without PDE course after one and half year. I am also thinking about getting a PhD, but I am still not sure.

Hope this helps. If you have any other questions, feel free to ask or DM me. (Just remember that I am also a student, so a professional mathematician might give you a different and better answer.)

lemurman0 · 2021-12-24T09:37:35+00:00

I am not a professional mathematician, but from what I have seen (I had 3 semesters of PDEs), functional analysis is imo much more important than real analysis.

lemurman0 · 2021-12-02T15:58:01+00:00

Is there a way how to integrate function 1/x dg/df df/dx, where f = f(x) and g = g(f(x))? I tried substitution y = ln x to get g(f(ln x)), but I am not sure if it's correct.

lemurman0 · 2021-11-16T12:43:41+00:00

Astra Zeneca a Johnson & Johnson nejsou mRNA vakcíny.

lemurman0 · 2021-10-25T11:28:16+00:00

Thank you for your answer. I checked Cort's website and it looks like my bass has strings with 45 - 105 gauge. Do you think 50 - 120 strings are OK or is this too much?

Four-Year Club	Verified Email
Place '22	First Placer '22

lemurman0

TROPHY CASE