Recent content by Denis99

I have to work with definition like this one from definition of inner space in here https://en.m.wikipedia.org/wiki/Inner_product_space (in part Definition)

Let $$<x, x>=3x_{1}^2+2x_{2}^2+x_{3}^2-4x_{1}x_{2}-2x_{1}x_{3}+2x_{2}x_{3} $$ be a quadratic form in V=R, where $$x=x_{1}e_{1}+x_{2}e_{2}+x_{3}e_{3}$$ (in the base $${e_{1},e_{2},e_{3}}$$. Find the inner product corresponding to this quadratic form. Is this that easy that you have to change ''...

Thank you for your answer :) I was thinking about this, but is there a way to calculate limit of this fraction? Sinuses are problematic for me in this limit.

Find Radius and Interval of Convergence for $$\sum_{1}^{\infty}(\frac{x}{sinn})^{n}$$. I don`t have any ideas how to do that :/

Thank you very much! That solution is brilliant :)

Like in the topic, the goal is to show that def(SoT) <= def(T)+def(S) (where def(P)=dim(KerP), T,S:V -> V are linear transformations and V<infinity). Unfortunately Ker(SoT) isn`t a subset of Ker(S)+Ker(T), so I try to solve this problem starting with that Ker(T) is subset of Ker(SoT), but I...