Eigenvalues and Eigenvectors
Bases
The main property of a
Basis
is that every point in the space can be expressed as a linear combination of elements in the basis
Span
The span of a set of vectors is simply
the set of points that can be reached by walking in the direction of these vectors in any combination
A basis is a minimal spanning set
Eigenbases
Some basis are more useful than others
Eigenbases
- A special way of linear transformation with respect to a basis that sends a parallelogram to another parallelogram with sides parallel to the original one. The basis is streched in the two directions (in the below case) which is called eigenbasisIn the linear transformation, the two vectors in the basis are called Eigenvectors and the streching factor are called Eigenvalues