# What does it means "orthonormal" vector?

my teacher's slides say that

"The columns [u_1, u_2, . . . , u_m] of an orthogonal matrix are orthonormal".

The slides provide a rigorous definition of orthogonal matrix but they say nothing about orthonormal vectors.

What does it means?

• A set of vectors is called "orthonormal" if they are pairwise-orthogonal and each is of magnitude 1. Sep 23 at 16:10

The implied meaning is that the columns are each normal (length $$1$$) and are orthogonal to one another. You are right that a single vector cannot be orthonormal.