All Questions

Like the title says, if an under-determined system of linear equations does have at least one positive solution, how to find it efficiently? Suppose we have an under-determined system: $$Ax = b$$ ...

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,\; \...

$\circ$ 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 = (x_{1},x_{2},.....

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 $M_k$...

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 ...

I'm reading a paper that outlines the calculation of a covariance matrix like the following: $C=\displaystyle\sum^{N_b}_{i=1}\vec{x}_i\vec{x}_i^T$ What is the order of this matrix? My interpretation ...