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# cov() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

C = cov(A) returns the covariance. If A is a vector of observations, C is the scalar-valued variance.If A is a matrix whose columns represent random variables and whose rows represent observations, C is the covariance matrix with the corresponding column variances along the diagonal.C is normalized by the number of observations-1. If there is only one observation, it is normalized by 1.If A is a scalar, cov(A) returns 0. If A is an empty array, cov(A)returns NaN.exampleC = cov(A,B) returns the covariance between two random variables A and B. If A and B are vectors of observations with equal length, cov(A,B) is the 2-by-2 covariance matrix.If A and B are matrices of observations, cov(A,B) treats A and B as vectors and is equivalent to cov(A(:),B(:)). A and B must have equal size.If A and B are scalars, cov(A,B) returns a 2-by-2 block of zeros. If A and B are empty arrays, cov(A,B) returns a 2-by-2 block of NaN.exampleC = cov(___,w) specifies the normalization weight for any of the previous syntaxes. When w = 0 (default), C is normalized by the number of observations-1. When w = 1, it is normalized by the number of observations.exampleC = cov(___,nanflag) specifies a condition for omitting NaN values from the calculation for any of the previous syntaxes. For example, cov(A,'omitrows') will omit any rows of A with one or more NaN elements.

C = cov(A) exampleC = cov(A,B) exampleC = cov(___,w) exampleC = cov(___,nanflag) example

Covariance of MatrixOpen This ExampleCreate a 3-by-4 matrix and compute its covariance.A = [5 0 3 7; 1 -5 7 3; 4 9 8 10]; C = cov(A) C = 4.3333 8.8333 -3.0000 5.6667 8.8333 50.3333 6.5000 24.1667 -3.0000 6.5000 7.0000 1.0000 5.6667 24.1667 1.0000 12.3333 Since the number of columns of A is 4, the result is a 4-by-4 matrix.Covariance of Two VectorsOpen This ExampleCreate two vectors and compute their 2-by-2 covariance matrix.A = [3 6 4]; B = [7 12 -9]; cov(A,B) ans = 2.3333 6.8333 6.8333 120.3333 Covariance of Two MatricesOpen This ExampleCreate two matrices of the same size and compute their 2-by-2 covariance.A = [2 0 -9; 3 4 1]; B = [5 2 6; -4 4 9]; cov(A,B) ans = 22.1667 -6.9333 -6.9333 19.4667 Specify Normalization WeightOpen This ExampleCreate a matrix and compute the covariance normalized by the number of rows.A = [1 3 -7; 3 9 2; -5 4 6]; C = cov(A,1) C = 11.5556 5.1111 -10.2222 5.1111 6.8889 5.2222 -10.2222 5.2222 29.5556 Covariance Excluding NaNOpen This ExampleCreate a matrix and compute its covariance, excluding any rows containing NaN values.A = [1.77 -0.005 3.98; NaN -2.95 NaN; 2.54 0.19 1.01] A = 1.7700 -0.0050 3.9800 NaN -2.9500 NaN 2.5400 0.1900 1.0100 C = cov(A,'omitrows') C = 0.2964 0.0751 -1.1435 0.0751 0.0190 -0.2896 -1.1435 -0.2896 4.4104