Principles of Quantum Mechanics · Problem 1.3.1

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · gram-schmidt-orthogonalization

Problem

Form an orthonormal basis in two dimensions starting with

\vec{A} = 3\hat{i} + 4\hat{j}

and

\vec{B} = 2\hat{i} - 6\hat{j}

. Can you generate another orthonormal basis starting with these two vectors? If so, produce another.