Linear Algebra/Orthogonal Sets

Orthogonal Sets


Given a set  , where   through   are nonzero vectors of the same dimension, is an orthogonal set if


where  .

So, for example, if one has a set of 3 vectors with the same dimension (for example  ) and taking the dot product of each vector with each other vector all equal zero, it is an orthogonal set. This is illustrated below.

Example of Orthogonal Set



We see that




Thus,   is an orthogonal set of vectors.