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Suppose we have a [itex]mxn[/itex] matrix, where each row is an observation and each column is a variable. The [itex](i,j)[/itex]-element of its covariance matrix is [itex]\mathrm{E}\begin{bmatrix}(\vec{X_i} - \vec{\mu_i})^t*(\vec{X_j} - \vec{\mu_j})\end{bmatrix}[/itex], where [itex]\vec{X_i}[/itex] is the column vector corresponding to a variable (its elements are the observations) and [itex]\vec{\mu_i}[/itex] is the corresponding mean vector formed by one repeated element which is the mean value of the variable, calculated from its observations. Hence, the covariance matrix is a symmetric [itex]nxn[/itex] matrix.

Is the argument correct? Thank you for answering me.

Another question: could we just replace the "[itex]E[/itex] sign" with the division by the total number of observation, [itex]m[/itex]?

Is the argument correct? Thank you for answering me.

Another question: could we just replace the "[itex]E[/itex] sign" with the division by the total number of observation, [itex]m[/itex]?

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