Linear Algebra/Orthogonal Sets

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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.