Verifying eigenvectors and eigenvalues with examples

Understanding eigenspaces and finding their basis

Verifying eigenvectors and finding eigenvalues of a 2x2 matrix

Verifying an eigenvector and finding the eigenvalue of a 3x3 matrix

Verifying an eigenvalue and finding its corresponding eigenvector

Finding a basis for the eigenspace of a 3x3 matrix

Proving the only eigenvalue of a nilpotent matrix A² = 0 is zero

Proving the inverse of an eigenvalue belongs to the inverse matrix