# Eigenvectors

- Vectors that stay on their own span during a transformation.
- Can be considered the axis of rotation for a rotation transformation.
- A v = (lambda) v =(lambda) * I
- A - (lambda ) v gives 0
- Non zero solution v soluton
- Product of a matrix with a non zero vector will only be possible if it reduces dimension
- If there are no real number solutions, then there are no eigenvectors
- Diagonal matrix – all the basis vectors are eigen vectors, with eigen values as the diagonal values