##  [Covariance Operator](/covariance-operator) 

  ##  [Covariance Operator](https://natural.quantumdictionary.io/covariance-operator-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A linear mapping that encodes second-moment relations of a random element: for finite-dimensional vectors it is the covariance matrix seen as a linear operator, and in function or Hilbert spaces it is the symmetric positive semidefinite operator that maps a test direction to the covariance with the projection along that direction.