Howtosignalprocessing
- Are poles equal to eigenvalues?
- What are eigen values How are these related to the closed loop poles?
- What happens if all eigenvalues are equal?
- Are eigen values of matrix A then trace of A is equal to?
Are poles equal to eigenvalues?
Since the roots of the denominator of H(z) are the system's poles, the eigenvalues of A and the poles of H(z) are equivalent.
What are eigen values How are these related to the closed loop poles?
The eigenvalues of the system determine completely the natural response (unforced response). In control theory, the response to any input is a combination of a transient response and steady-state response. Therefore, a crucial design parameter is the location of the eigenvalues, or closed-loop poles.
What happens if all eigenvalues are equal?
From the Jordan decomposition theorem, we see that A=V−1JV, with J having constant diagonal entries, which are the eigenvalues of A. However, if the matrix has all the eigenvalues the same, and is in addition normal, you know that it is a constant multiple of identity matrix.
Are eigen values of matrix A then trace of A is equal to?
6.4 Properties of eigenvalues and eigenvectors. The trace of a matrix A, designated by tr(A), is the sum of the elements on the main diagonal. The sum of the eigenvalues of a matrix equals the trace of the matrix.
