How can one modify only the diagonal entries of a matrix so that one eigenvector becomes orthogonal to a given vector? – math.stackexchange.com

Let $A=[a_{ij}]\in\mathbb{R}^{n\times n}$ be a real symmetric positive definite matrix, and let $b\in\mathbb{R}^n$ be a given vector. Assume that no eigenvector of $A$ is orthogonal to $b$, i.e., for ...