Recent content by Constantinos

hmm... yes I think you are right! How did I miss this intuition? It would be the same thing as, for example, finding an object closer to the galactic core and going towards it. The galaxy wouldn't grow much larger in my point of view of course. Hmm, I think I will now draw some geometric...

Hey! Here's a question. This is Mercury as seen from some telescope during one of its transits The white disk in the background is the Sun. So suppose now that I am where this telescope is and start approaching Mercury. As I approach, both the Sun and Mercury would become larger from my point...

Hey! I was wondering, is it a bad idea to solve a math problem mentally instead of writing it down? I recently got a copy of "Understanding Analysis" and try to read it cover to cover using this method. Should I? It resembles blindfold chess in a way.

Well I haven't been learning about any matrices lately! This question arose on a stochastic processes exercise, were a certain Z = BX + d where X is a random vector of uncorrelated Gaussian random variables. The exercise asks what must Β be for the Ζ variables to still remain uncorrelated. This...

Hey! So here's the question: Homework Statement Let \mathbf{B} \in \mathbb{R}^{n \times n} be some square matrix we can choose and \mathbf{D} \in \mathbb{R}^{n \times n} be some given diagonal matrix with positive diagonal elements. For what matrices \mathbf{B} is the product...

hmm yes I think you are right, thanks for your help! I couldn't get anywhere because I was thinking in terms of whole rows, instead of their parts that are into a diagonal block. Of course if a set of block-rows(or how else to call that?) from the diagonal blocks are L.I then the corresponding...

Hey! I found this interesting theorem in a textbook, but I was unable to find a proof for it neither in the web nor on my own Homework Statement The rank of a block triangular matrix is at least and can be greater than the triangular blocks. proof? specificaly, look here: pp. 25...

Hey! Let M and N be two natural numbers and N>M. I want to build a set A with N vectors of size M such that each subset S of A, where |S| = M, contains linearly independent vectors. Another way to put it is that every S should be a basis for R^M. Any ideas? Thanks!

Hey! I have a certain problem. Let M ≥ 4 be an even number and consider the set [0,1,...\frac{M}{2}-1]. The problem is to put those numbers two times in each row of an M x (M choose 2) matrix, such that all possible combinations of entries that contain a pair of the same number occur just once...

Hey! Can anyone help me with visualizing this concept or explaining it in more intuitive terms? : thanks!

anyone?

Hey! I was just wondering if anyone happens to know of a good forum where the matters of the title are being discussed, or if you know any other kinds of resources on the subject. I'm pretty clueless on the subject and it seems like a good thing to start gaining some knowledge about.

This thread would be nice for listing study subjects that no matter how the world changes, the knowledge gained is never obsolete. Mathematics is one example. Whatever happens to the world, 1+1 = 2 and everything that spans from it. Physics is another one. Physics will be relevant until the...

Instead of the dilemma independent vs dependent, perhaps a more useful way to see things is your degree of "resilience". What I mean by that is that it doesn't matter if you are dependent on many other people for your resources (i.e material goods of any kind), but that a single individual's...

Interesting discussion! Another similar concept is that of "western canon", a list of works from the very old(Epic of Gilgamesh) to the 21st century writers, that are said to be most influential to western culture. A known literary critic Harold Bloom has composed such a list...