Covariance matrix

Dependencies:

  1. Random variable
  2. Cross-covariance matrix

Let $X = [X_1, X_2, \ldots, X_n]$ be a sequence of random variables. Then the covariance matrix of $X$, an $n$-by-$n$ matrix, is defined as the cross-covariance matrix of $X$ with itself: $\operatorname{Var}(X) = \operatorname{Cov}(X) = \operatorname{Cov}(X, X)$

Dependency for:

  1. Standard multivariate normal distribution

Info:

Transitive dependencies:

  1. /measure-theory/linearity-of-lebesgue-integral
  2. /measure-theory/lebesgue-integral
  3. /sets-and-relations/de-morgan-laws
  4. /sets-and-relations/countable-set
  5. /analysis/topological-space
  6. Group
  7. Ring
  8. Field
  9. Vector Space
  10. σ-algebra
  11. σ-algebra is closed under countable intersections
  12. Measure
  13. Probability
  14. Generated σ-algebra
  15. Measurable function
  16. Borel algebra
  17. Generators of the real Borel algebra (incomplete)
  18. Random variable
  19. Expected value of a random variable
  20. Linearity of expectation
  21. Covariance of 2 random variables
  22. Linearity of expectation for matrices
  23. Cross-covariance matrix