The sample covariance matrix is $S = \frac{1}{n} \sum_{i=1}^{n} (X^{(i)}-\bar{X}) (X^{(i)}-\bar{X})^T$. Note that for normally distributed random variables, $S$ is the maximum likelihood estimator (MLE) for the covariance matrix. This is different from the unbiased estimator, which uses a denominator of $n-1$ instead of $n$.
Sample data is input as a matrix or a list. The rows of the matrix or the elements of the list are observation vectors.
i1 : L= {{1,2,1,-1},{2,1,3,0},{-1, 0, 1, 1},{-5, 3, 4, -6}};
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i2 : sampleCovarianceMatrix(L)
o2 = | 115/16 -13/8 -29/16 47/8 |
| -13/8 5/4 7/8 -11/4 |
| -29/16 7/8 27/16 -21/8 |
| 47/8 -11/4 -21/8 29/4 |
4 4
o2 : Matrix QQ <--- QQ
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i3 : U= matrix{{1,2,1,-1},{2,1,3,0},{-1, 0, 1, 1},{-5, 3, 4, -6}};
4 4
o3 : Matrix ZZ <--- ZZ
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i4 : sampleCovarianceMatrix(U)
o4 = | 115/16 -13/8 -29/16 47/8 |
| -13/8 5/4 7/8 -11/4 |
| -29/16 7/8 27/16 -21/8 |
| 47/8 -11/4 -21/8 29/4 |
4 4
o4 : Matrix QQ <--- QQ
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The object sampleCovarianceMatrix is a method function.