Definition
Throughout this article, boldfaced unsubscripted X and Y are used to refer to random vectors, and unboldfaced subscripted Xi and Yi are used to refer to random scalars.
If the entries in the column vector
are random variables, each with finite variance, then the covariance matrix Σ is the matrix whose (i, j) entry is the covariance
where
is the expected value of the ith entry in the vector X. In other words, we have
The inverse of this matrix, is the inverse covariance matrix, also known as the concentration matrix or precision matrix; see precision (statistics). The elements of the precision matrix have an interpretation in terms of partial correlations and partial variances.
Read more about this topic: Covariance Matrix
Famous quotes containing the word definition:
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)