MATLAB Function Reference |

**Syntax**

**Description**

```
C = cov(x)
```

where `x`

is a vector returns the variance of the vector elements. For matrices where each row is an observation and each column 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.

```
C = cov(x,y),
```

where `x`

and `y`

are column vectors of equal length, is equivalent to `cov([x y])`

.

**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**

`xcorr`

, `xcov`

in the Signal Processing Toolbox

coth | cplxpair |