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in case of system represented by a transfer function. the roots of the denominator are eigen values and their value is important to gain insigh in the stability of the systems. i think they have other advantages also but cant fgure it out..
regards
Suppose you have a square matrix A and you have to find a function f(A). The eigen values are the solution of the characteristic equation |A-λI| = 0, which is a function F(λ). From this you can find any function of A using CH theorem.
One very important use of eigenvalues is finding the principal axes of a rotating system using moment of inertia tensor. Eigen values are required to diagonalize the matrix of the tensor to find them.
To sohailkhanonline: Could you please be a little more clear, because what you are saying sounds interesting. You say, the roots of the denominator of a transfer function are eigenvalues. But eigenvalues of what? To find the eigenvalues you should have a matrix, so what is that matrix for your case.
Added after 1 minutes:
To subharpe: I think it is not a must to have a square matrix for eigenvalue calculation.
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