# Diagonalization

Let be an matrix, and let be the eigenvectors corresponding to the eigenvalues  satisfying

 (12)

Then we can define a diagonal matrix  and a matrix  respectively by

 and (13)

Together we can summarize the equations of eigenvectors as

Furthermore, if are linearly independent, the matrix  is invertible, and therefore, we obtain

 (14)

The matrix  is said to be diagonalizable if has the above expression.

Subsections

Department of Mathematics