Let's say we got $3$ vectors given and we need to check if they are an orthonormal basis of some vector space. How would that be done quickly? I have read on several sites on the Internet and here is my summary, correct me if I'm wrong please:
- All vectors need to be linearly independent.
- Vectors are perpendicular aka orthogonal to each other (if $3$ vectors given, I have to do it as pairs of $2$, right?).
- Each vector has length $1$.