Recent content by JFerreira

If you haven't found the answer to your question, please see this thread. It talks about the fact that the eigenvalues of the adjacency matrix describe closed walks on the graph, and much more. You can find other results, searching, for instance, for "graph Laplacian matrix eigenvalues " on...

In paper (2nd link) section 3 claim 1, the matrix F is a permutation matrix. This matrix F has the given form because the vector ##v=[1\,\, t\,\, t^2]## was rewritten as ##u=[t \,\,t^2\,\, 1]##. This is represented by the matrix F, which is the identity matrix, rewritten with colluns in...

I like to play with some iterations functions to produce fractals. And I also like to think about the dynamics of this process. This means that this questions is very interesting to me, and I really want to know if you find some thing on this direction. I like to think on Newton's method in a...

When I need to solve an equation like $$f(x)=0,$$ and I can't find a fixed point iteration function that works, I try to see the equation as the minimization problem $$0=\min_{x}g(x),\qquad g(x)=\frac{1}{2}\|f(x)\|^2.$$ Then I can try to solve it by using some numerical methods to handle with...

Try $$f(x)=\frac{1}{\sqrt{1-x}}-3.$$

Useful functions to handle with similar question is $$f(x)=\frac{x}{1-|x|}$$ and $$g(x)=\frac{x}{1+|x|},$$ with some change of variable. Note that ##x## can be a vector, like one in ##\mathbb{R}^2##, for instace. Try to search to "\(\frac{x}{1-|x|}\)" on SearchOnMath.

Geogebra can help you see the graphs: https://www.geogebra.org/graphing/sfgvm5zu

Hi everyone, I founded this discussion very interesting, so a search if someone did it before. "A is linear transformation from a finite dimensional vector space to itself. AB=I amounts to saying A is surjective, hence it is bijective and has a left inverse C, so that CA=I. Of course...