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Saturday, June 4, 2016

A (Very) Useful Formula for Matrix Inversion

Here is a very useful formula for matrix inverse, I think the first time I saw it is from Prof. John Cioffi's book.

(A+BD1C)1=A1A1B(D+CA1B)1CA1


let me give one example of how it can be used. Assuming that Ruu=h2hh2+λI where h2 is a vector. Then we have

R1uu=λ1I1λ2+λhh2h2h2hh2


By using this formula, the end result turns out to be much simpler than where it starts from.

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