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A Beautiful 2 by 2 Matrix Identity

While working on a variation of the RcppDynProg algorithm we derived the following beautiful identity of 2 by 2 real matrices:

The superscript “top” denoting the transpose operation, the ||.||^2_2 denoting sum of squares norm, and the single |.| denoting determinant.

This is derived from one of the check equations for the Moore–Penrose inverse and we have details of the derivation here, and details of the messy algebra here.

Categories: Mathematics Opinion Tutorials

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Data Scientist and trainer at Win Vector LLC. One of the authors of Practical Data Science with R.

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