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Solving matrix equation in Matlab,

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Hi Matlab,
I'm currently doing research on macroeconomic variables; hence attempting to solve an matrix equation in Matlab ( see attached photo, marked with yellow (following VECM Analysis in JMulTi July 5, 2005, page 26). Does anyone know to calculate the value for sigma (marked with yellow)?
I haven't attached a code, since, at the moment, don't know how to calculate it in Matlab, hence any help greatly appreciated!
Best regards,

Accepted Answer

Chuguang Pan
Chuguang Pan on 7 Mar 2024
Using vectorization operator vec, which transfer a matrix to a column vector through stacking matrix's columns vertically. There is a useful equation in this context.
, where represents kronecker product.
The matrix equation can be converted to the following vector equation,
This vector equation can be solved with MATLAB, and you can reshape the to matrix .
Chuguang Pan
Chuguang Pan on 7 Mar 2024
I am not familiar with how the estimator of the covariance matrix is obtained. The variable estSigma is just named referred to the image @Simon Christensen.

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