Linear Algebra/Orthogonal Sets

Orthogonal SetsEdit

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 SetEdit

 

 

We see that

 

 

 


Thus,   is an orthogonal set of vectors.