Find eigenvalues and eigenvectors of the matrix
By transforming the matrix in the basis of eigenvectors, show explictly that the matrix can diagonalized in the eigenvector basis.
The definition of an eigenvalue is:
AX = LX where L is the eigenvalue (lambda)
Which can be rewritten:
(LI-A)X = 0, where I is the identity matrix.
So, that brings us to the characteristic polynomial in our 5 line review:
c(x) = det(xI - A)
The eigenvalues are the roots of this ...
Eigenvalues of a matrix are found. Diagonalization is shown.