Real spectral theorem
= Real spectral theorem
Every real symmetric matrix is orthogonally diagonalizable. Distinct eigenspaces are orthogonal because symmetry gives $\lambda\langle u,v\rangle=\mu\langle u,v\rangle$.
= Real spectral theorem
Every real symmetric matrix is orthogonally diagonalizable. Distinct eigenspaces are orthogonal because symmetry gives $\lambda\langle u,v\rangle=\mu\langle u,v\rangle$.