Lysario – by Panagiotis Chatzichrisafis

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

Archive for Januar, 2010

In [1, p. 34 exercise 2.11] we are asked to find the eigenvalues of the circulant matrix given in [1, (2.27),p.22]. read the conclusion >
In [1, p. 34 exercise 2.10] it is asked to prove that if \mathbf{A} is a complex n \times n positive definite matrix and \mathbf{B} is a full rank complex m \times n matrix with m \leq n, then \mathbf{BA}\mathbf{B}^H is also positive definite. read the conclusion >
In [1, p. 34 exercise 2.9] we are asked to prove that the rank of the complex n\times n matrix
\mathbf{A}=\sum\limits_{i=1}^{m} d_{i}\mathbf{u}_i\mathbf{u}_{i}^{H} (1)

where the \mathbf{u}_i are linearly independent complex n \times 1 vectors and the d_i‘s are real and positive, is equal to m if m \leq   n. Furthermore we are asked what the rank equals to if m > n. read the conclusion >

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