Question

Symmetric matrices can be diagonalizable if they have n independent eigenvectors.
My doubt is that Do Every Symmetic real Matrix have n independent eigenvectors ?

Answer 1

Yes, but the proof is not easy. Prof Strang has put a proof in his book "An Introduction to Linear Algebra" on page 335, in which he applies Schur's theorem.

Answer 2

@forestconrad , thank you , it is a huge help to me