Answer to Question #246805 in Linear Algebra for Leroy

Question

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

Assuming A is positive definite, consider the oblique projection framework where Wk = AKk,

and show that Span{r0,r1,...,rk−1}= Kk (A,r0)

Where ri are the residuals and Kk is the Krylov space