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,
I want to calculate the total variation \left \| f \right \|_{V(\Omega)} with \Omega=(-1,1) and f(x)=\mathrm{sgn}(x).
The total variation of a function is defined as follows:
\left \| f \right \|_{V(\Omega)} :=\sup\left \{ \int_\Omega f\ \mathrm{div} (v)\ dx \ | \ v \in...
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...