MATLAB Function Reference |

**Syntax**

**Description**

`cov(X)`

, if `X`

is a vector, returns the variance. For matrices, where each row is an observation, and each column is a variable, `cov(X)`

is the covariance matrix. `diag(cov(X))`

is a vector of variances for each column, and `sqrt(diag(cov(X)))`

is a vector of standard deviations. `cov(X,Y)`

, where `X`

and `Y`

are vectors of equal length, is equivalent to `cov([X(:) Y(:)])`

.

`cov(X)`

or `cov(X,Y)`

normalizes by N-1 where N is the number of observations. This makes `cov(X)`

the best unbiased estimate of the covariance matrix if the observations are from a normal distribution.

`cov(X,1)`

or `cov(X,Y,1)`

normalizes by N and produces the second moment matrix of the observations about their mean. `cov(X,Y,0)`

is the same as `cov(X,Y)`

and `cov(X,0)`

is the same as `cov(X)`

.

**Remarks**

`cov`

removes the mean from each column before calculating the result.

The *covariance* function is defined as

where is the mathematical expectation and .

**Examples**

Consider `A = [-1 1 2 ; -2 3 1 ; 4 0 3]`

. To obtain a vector of variances for each column of `A`

:

Compare vector `v`

with covariance matrix `C`

:

The diagonal elements `C(i,i)`

represent the variances for the columns of `A`

. The off-diagonal elements `C(i,j)`

represent the covariances of columns `i`

and `j`

.

**See Also**

`corrcoef`

, `mean`

, `median`

, `std`

, `var`

`xcorr`

, `xcov`

in the Signal Processing Toolbox

coth | cplxpair |

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