Category Archives: Math: Vectors and matrices

Useful properties of idempotent matrices

Idempotent matrices appear in regression analysis, so can’t be ignored. Here are commonly used properties: Properties of idempotent matrices The eigenvalues of an idempotent matrix are 0 and 1. The rank of an idempotent matrix is equal to its trace … Continue reading

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Independence of quadratic forms

The following result is useful for deriving F-tests. Independence of quadratic forms for orthogonal projection matrices Let , and let matrices and be orthogonal projections – and as such they must be symmetric and idempotent. Then, the quadratic forms and … Continue reading

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Matrix differentiation for econometrics: function of a vector and quadratic form

Let f be a scalar function of a vector . Then partially differentiating with respect to each and arranging the derivatives into a column vector gives us Vector differentiation Suppose is a linear function of the column vector where is … Continue reading

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