Answer to Question #246807 in Linear Algebra for Leroy

Question

Consider the linear system Ax = b where A ∈Rn×n is non-singular and b ∈Rn.

assume A is symmetric (but not necessarily positive definite), and consider

again the oblique projection framework.

Wk = AKk

Where AKk is the Krylov space

Show that 〈r0,rk〉= ‖rk‖^2