Lysario – by Panagiotis Chatzichrisafis
"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"
Archive for November, 2009
Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”,p. 34 exercise 2.7
Author: Panagiotis20 Nov
In exercise [1, p. 34 exercise 2.7] it is requested to find the inverse of the real symmetric Toeplitz matrix
and show that it is symmetric and persymmetric. read the conclusion >
![\mathbf{A} = \left[ {\begin{array}{*{20}c}
1 & { - a} & {a^2 } \\
{ - a} & 1 & { - a} \\
{a^2 } & { - a} & 1 \\
\end{array}} \right]](https://lysario.de/wp-content/cache/tex_7d981ef3134de2499a9848c900a503e7.png) | (1) | ||
and show that it is symmetric and persymmetric. read the conclusion >
Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”,p. 34 exercise 2.6
Author: Panagiotis16 Nov
In problem [1, p. 34 exercise 2.6] we are asked to prove that if 
and 
are complex 
Hermitian matrices and 
is positive semidefinite, then ![\left[\mathbf{A}\right]_{ii} \geq \left[\mathbf{B}\right]_{ii}](https://lysario.de/wp-content/cache/tex_3652289cddad029917d54c1a0ed7c8cd.png)
.
read the conclusion >
and are complex Hermitian matrices and is positive semidefinite, then .
read the conclusion >