MATLAB Function Reference
cov

Covariance matrix

Syntax

• ```C = cov(X)
C = cov(x,y)
```

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`:

• ````v = diag(cov(A))`'
v =
10.3333    2.3333    1.0000
```

Compare vector `v` with covariance matrix `C`:

• ```C =
10.3333   -4.1667    3.0000
-4.1667    2.3333   -1.5000
3.0000   -1.5000    1.0000
```

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`.

`corrcoef`, `mean`, `std`
`xcorr`, `xcov` in the Signal Processing Toolbox