# Linear Algebra/Orthogonal Sets

## Orthogonal Sets

editGiven 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

edit

We see that

Thus, is an orthogonal set of vectors.