Hi, Suman,
I think I don't really understand your question, because in such different fields, the eigenvalues of the matrices might have really different meanings.
I study multibody dynamics, and in my area, linearized systems are described in the state space form as in the equation below:
{dx/dt} = [A]{x} + [B]{u(t)}
,where [A] and [B] are constant matrices ([A] is n by n ans [B] is n by p, where n is the number of states and p the number of inputs), {x} is the array of states and {u(t)} the array of inputs.
In order to solve the homogeneous problem ({u(t)} = {0}), we need to calculate the eigenvalues of the matrix [A]. From these eigenvalues it is possible to verify how the system behaves. It follows that:
Real eigenvalues:
Real negative eigenvalue -> Stable and non oscillatory transient reponse
Real positive eigenvalue -> Unstable and non oscillatory transient reponse
Null eigenvalue -> rigid body motion
Complex conjugate pairs:
Negative real part -> Stable, decaying and oscillatory transient reponse
Positive real part -> Unstable, increasing and transient reponse
Null real part -> Sinusoidal transient reponse
Although it is not about all the areas you mentioned, I hope it helps you.
Best wishes,
Vinícius
Thank You for Your precious Reply. Prof. Vinícius Simionatto, I got some clues from your statements, suggest me some real life application of such Eigen values of Matrix.
Thank You for Your precious Reply Prof. . Viswanath Devan, You have given me some ideas regarding Eigen value in image processing. I have calculated eigen value of some square simatric matrix {matrix , which isthe representation of any robotic arm movement }. Will I apply it to image processing. If so, then suggest me how could I apply Eigen values of matrices in image processing with the help of neural network
Suman, do you have a certain application in mind or problem you want to solve? If so, please write more details in your question which allows people to give you more detailed answers.
Regarding images processing, eigenvalues and neural networks, i assume you want to somehow do object detection or classification.
The eigenvalues are used in many computer vision algorithms, as already described by Viswanath. You need to look at the eigenvalues always in the context of the algorithm, e.g. feature extraction. The eigenvalues and/or the features can then be used as input to a neural network to do object detection / classification.
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