# Lysario – by Panagiotis Chatzichrisafis

"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"

## Archive for November, 2009

In exercise [1, p. 34 exercise 2.7] it is requested to find the inverse of the real symmetric Toeplitz matrix
 $\mathbf{A} = \left[ {\begin{array}{*{20}c} 1 & { - a} & {a^2 } \\ { - a} & 1 & { - a} \\ {a^2 } & { - a} & 1 \\ \end{array}} \right]$ (1)

and show that it is symmetric and persymmetric. read the conclusion >
In problem [1, p. 34 exercise 2.6] we are asked to prove that if $\mathbf{A}$ and $\mathbf{B}$ are complex $n\times n$ Hermitian matrices and $\mathbf{A}-\mathbf{B}$ is positive semidefinite, then $\left[\mathbf{A}\right]_{ii} \geq \left[\mathbf{B}\right]_{ii}$. read the conclusion >