Why are the eigenvalues of a matrix so important?

Status
Not open for further replies.

senaydud

Advanced Member level 4
Joined
Jun 23, 2008
Messages
112
Helped
11
Reputation
22
Reaction score
4
Trophy points
1,298
Activity points
1,965
Why are the eigenvalues of a matrix is that important?
 

eigenvalue denominator

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
 

moment of inertia and eigenvalues

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.
 

how to find transfer function from eigenvalues

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.
 

how eigenvalues relates to transfer function

To senaydud:

I don't know if any non-square matrix can have a eigenvalue. Can you please be detailed on that?

With thanks
 

    senaydud

    Points: 2
    Helpful Answer Positive Rating
Eigenvalues

yes I have checked with the matlab and it requires the matrix to be a square matrix. You are right
 

Status
Not open for further replies.

Similar threads

Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…