Linear Algebra/Orthogonal Sets

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Orthogonal Sets[edit]

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[edit]

We see that

Thus, is an orthogonal set of vectors.