Transposes correspond to integration by parts, and the question of whether A^T*A has an inverse can get involved. Also for infinite matrices the analogies hold

Transposes correspond to integration by parts, and the question of whether A^T*A has an inverse can get involved. Also for infinite matrices the analogies hold more readily, see the observation due to Alan Edelman on page 8 of https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf