Eigenvalues of a vector

1. What are eigenvalues of a vector?
2. Does a vector have eigenvalues?
3. What do eigenvalues and vectors tell us?

What are eigenvalues of a vector?

Eigenvalues are the special set of scalar values that is associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed as characteristic roots. It is a non-zero vector that can be changed at most by its scalar factor after the application of linear transformations.

Does a vector have eigenvalues?

Therefore, any vector that points directly to the right or left with no vertical component is an eigenvector of this transformation, because the mapping does not change its direction. Moreover, these eigenvectors all have an eigenvalue equal to one, because the mapping does not change their length either.

What do eigenvalues and vectors tell us?

This line of best fit, shows the direction of maximum variance in the dataset. The Eigenvector is the direction of that line, while the eigenvalue is a number that tells us how the data set is spread out on the line which is an Eigenvector.