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.© BrainMass Inc. brainmass.com March 4, 2021, 5:48 pm ad1c9bdddf
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. Transforming a matrix in the basis of eigenvectors are determined.