Worked examples

Eigenvalues, eigenvectors and diagonalization

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Eigenvalues and eigenspaces of matrices of order 2
• 2Eigenvalues and eigenspaces of matrices of order 3
• 3Diagonalization with the diagonalizing matrix
• 4Diagonalizability checks with the multiplicity criterion
• 5Diagonalizability of matrices with a parameter
• 6Powers of diagonalizable matrices
• 7Eigenvalues of endomorphisms and matrices with given eigenvectors