Is any real symmetric positive definite matrix similar to a triadiagonal symmetric positive definite matrix?
From Householder lemma it is known that if $B$ is symmetric, there exists a orthogonal matrix $H$ such that $C=H^\top B H$ is triadiagonal symmetric. The question is whether $C$ is definite positive; it has the same (positive) eigenvalues as $B$ so I would say yes.
Is this correct?