Please explain the examples of matrixx taken below in the notes

one more thing to remember, you can only take k1, k2, k3 , such that, all the three Eigen vectors are linearly independent. and you know in 3D the Standard vectors are the one whic...

you can take any values for k1, k2 and k3. but there is a restriction that k1, k2, k3, all simultaneously couldn't be zero(because then the eigenvector would become zero vector, wh...