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BUILT-IN MATHEMATICA SYMBOL
Covariance
Covariance[v1, v2]
gives the covariance between the vectors 
and 
.
Covariance[m]
gives the covariance matrix for the matrix m.
Covariance[m1, m2]
gives the covariance matrix for the matrices 
and 
.
Covariance[dist]
gives the covariance matrix for the multivariate symbolic distribution dist.
Covariance[dist, i, j]
gives the 
covariance for the multivariate symbolic distribution dist.
Details
- Covariance[v1, v2] gives the unbiased estimate of the covariance between
and 
. - The lists
and 
must be the same length. - Covariance[v1, v2] is equivalent to (v1-Mean[v1]). Conjugate[v2-Mean[v2]]/(Length[v1]-1).
- For a matrix m with
columns, Covariance[m] is a 
×
matrix of the covariances between columns of m. - For an
×
matrix 
and an 
×
matrix 
, Covariance[m1, m2] is a 
×
matrix of the covariances between columns of 
and columns of 
. - Covariance works with SparseArray objects.
- Covariance[dist, i, j] gives Expectation[(xi-
i)(xj-j), {x1, x2, ...}
dist], where 
is the i
component of the mean of dist. - Covariance[dist] gives a covariance matrix with the
entry given by Covariance[dist, i, j].
New in 6 | Last modified in 8
