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| ``block toeplitz matrices''
by silence on 2003-08-27 09:56:13 |
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| 1. I am working with block Toeplitz matrices arising in the context of multivariate time-series data. I was wondering if anyone is aware of methods of qualitatively inspecting and analyzing such matrices? For example, what can one say about such matrices given their pseudospectra (spectral portrait)?
2. What exactly does the spectral radius (or even the full sequence of eigenvalues) convey about the matrix itself? That is, how does one interpret the concept of an "eigenvalue" for any matrix without talking about solving a linear system of equations and so on? Rephrased: Is there a qualitative or intuitive way to think about what eigenvalues represent in terms of the actual structure or geometry of a matrix?
3. In the case of block Toeplitz structures, suppose each block can be decomposed into at least one eigenvalue and associated eigenvector, then are the total number of eigenvalues in a block structure equivalent to the number of blocks necessarily? |
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