This function is based on trigonometric functions. Therefore, we use these trigonometric function as the basis of the frequency domain analysis. Eigenvalues show us a brief overview of the operation and its function.
Assume we have an input x and an output y, operator T is applied to the input x, then the result is the y. If eigenvalue exists, we could write it as the following.
This means, a transfer function in signal processing is eigenvalue of linear algebra. How great it is!
This is an overview of recently I understand about eigenvalue, eigenvector, eigenfunction, and transfer function. I hope this also helps someone.
I wrote this article, but, actually first one month I didn't understand this at all. I thank Alexander B. who is so patient and answered my stupid and similar questions every time.