Recent content by brian_m.

Thanks for your help. Now I have calculated Y^T A Y. It is: Y^T A Y = \begin{pmatrix} y & z \end{pmatrix} \begin{pmatrix} t \cdot I_n & x \\ x^T & t \end{pmatrix} \begin{pmatrix} y\\z \end{pmatrix} = \begin{pmatrix} y_1t+zx_1 & \cdots & y_nt+zx_n & y_1x_1+...+y_nx_n+zt...

Hello. Homework Statement Let x \in \mathbb R^n and t \in \mathbb R. Prove the following equivalence: \left \| x \right \|_2 \leq t \ \ \Leftrightarrow \ \ \begin{pmatrix} t \cdot I_n & x \\ x^T & t \end{pmatrix} \text{is positive semidefinite } Homework Equations \left...

Hello, is anybody here, who can explain to me how to compute the integral closure of a ring (in another ring)? Example: What is the integral closure of Z in Q(sqrt(2)) ? Thank you! Bye, Brian

Hi, how can I show that a field extension is normal? Here is a concrete example: L|K is normal, whereas L=\mathbb F_{p^2}(X,Y) and K= \mathbb F_p(X^p,Y^p) . p is a prime number of course. I have to show that every irreducible polynomial in K[X,Y] that has a root in L...