# Tagged Questions

**2**

votes

**2**answers

98 views

### Boundedness of ratio of linear functions

Consider the function
\begin{eqnarray}
f(x_1,x_2,\cdots, x_n) = \frac{\sum_{i}^{n}a_ix_i}{\sum_{i}^{n}b_ix_i},
\end{eqnarray}
over the set $S = \{x := (x_1,x_2,\cdots, x_n):-1 \leq x_i \leq 1,\; ...

**1**

vote

**0**answers

45 views

### Nontrivial Matrix-estimate

I try to proof the following estimate:
\begin{align}
h' W^{-1} H W^{-1} h \geq c h' H h \qquad c>0, \qquad\qquad (1)
\end{align}
where $h\in\mathbb{R}^{K-1}$ and ...

**1**

vote

**1**answer

131 views

### Eigenvalue problem with quadratic constraints

$\circ$ Consider the following eigenvalue problem : $$Ax=\lambda x \hspace{0.5cm} (1)$$
where matrice $A \in \mathbb{R}_{n \times n}$ is a positive semi-definite with eigenvectors $x = ...

**1**

vote

**0**answers

99 views

### Matrix Minimax problem

I have the equation $\Sigma_k(M_k{p_k})V=EV$, where the $M_k$ are n*n real Hermitian matrices, $V$ is a n*n eigenvector matrix, $E$ a dim-n energy eigenvector and the $p_k$ scalar parameters. The ...

**2**

votes

**2**answers

202 views

### Maximization of a matrix product by iterative methods

This might not be very difficult, but I think I may have gotten a little confused.
Suppose we are given a matrix A, and would like to find the vector x of modulus 1 which maximises the product xt A x ...