I often use $\mathbf u \cdot \mathbf v = u_1v_1+u_2v_2+u_3v_3$ in three dimensions, and similar for other dimensions.

Does this work in any basis?

Thanks!

1 Answers

This simplified version of the dot product *only* works in an orthonormal basis.

This is described in Section 3.3 in the Immersive Linear Algebra book.