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The [[variance-covariance matrix]] of the residuals is, by [[error propagation]], equal to <math>\mathbf{\left(I-H \right)^\top M\left(I-H \right) }</math>, where '''M''' is the variance-covariance matrix of the errors (and by extension, the observations as well). Thus, the [[residual sum of squares]] is a [[quadratic form (statistics)|quadratic form]] in the observations.
The eigenvalues of an idempotent matrix are equal to 1 or 0.<ref>C. B. Read, Encyclopedia of Statistical Sciences, Idempotent Matrices, Wiley, 2006</ref> Some other useful properties of the hat matrix are summarized in <ref>P. Gans, ''Data Fitting in the Chemical Sciences,'', Wiley, 1992.</ref>
== See also ==
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