In my opinion, you should specify your question. In what sphere od digital signal processing (the scientific direction, to which this forum is dedicated) are you going to use eigen vectors and eigen values? The ways of application are numerous, that's why the concrete question is needed.
Nevertheless, I'll give you 2 examples:
1) Method of digital spectral analysis, cales MUSIC is based on counting eigen vectors and eigen values
2) Principal component analysis. When you want to diminish the size of attributes space, while processing data files so that the variance between the vectors remains unchanged, you use PCA. The basis vectors of the new space coincede with the eigen vecors of the data's covariance matrix, whereas the eigen values of the covariance matrix correspond to the variances of the attributes. Instead of covariance matrix, corre;lation matrix may be used as well.
With respect,
Dmitrij