I was reading a book on quantum mechanics (thats branch of physics). There is this
theorem which I didn't understand. Now the theorem is about physical observable
quantities like energy,momentum etc.. In quantum mechanics , such physical
observable quantity is represented by an operator. In matrix mechanics , which is a
version of quantum mechanics , such operators are written mathematically as
matrices. So the theorem is basically about matrices. I am going to translate the
theorem in mathematical language , removing words which relate to physics.
Theorem-- If two matrices commute, they possess a common set of eigenvectors.
This is true for both degenerate and non-degenerate eigenvectors.
Now when we have non-degenerate eigenvectors , two such commuting matrices
happen to have common eigenvectors anyway. But I have a question about
degenerate case. In such case , how do we obtain the common eigenvectors ?