Isotropic position
From Infogalactic: the planetary knowledge core
In the fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is equal to the identity matrix.
Formal definitions
Let be a distribution over vectors in the vector space . Then is in isotropic position if, for vector sampled from the distribution,
A set of vectors is said to be in isotropic position if the uniform distribution[disambiguation needed] over that set is in isotropic position. In particular, every orthonormal set of vectors is isotropic.
As a related definition, a convex body in is in isotropic position if, for all vectors in , we have
See also
References
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