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Linear Algebra/Orthogonal Sets
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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.