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In the past I derived it as following: It is a little different approach. If it answers your question I will rewrite it in a proper LaTeX. Regarding your question about the steps in the derivation you presented, it is using the Woodbury Matrix Identity (Both 12.26 to 12.27 and 12.28 to 12.29). Related Answers: Deriving the Matrix Inversion Lemma for RLS ...

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