Dot product in general basis

QuestionsCategory: QuestionsDot product in general basis
mrtester asked 3 years ago

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
Tomas Akenine-Möller Staff answered 3 years ago

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.