- A vector will span a line passing through it. All points along the span, the line, can be reached by the vector using scalar multiplication.
- A matrix multiplication rotates and scales a vector
- A matrix multiplication will only scale a Eigen vector , without changing its span direction.
- A rotation matrix has no eigen vector. All vectors are rotated.
- A shear matrix has one eigen vector.
- There are matrices with one eigen value and many eigen vectors, like scaling all vectors on a plane.
- See these 3 matrices and one normal eigen vector eigen value matrix in 2GBAB.