I have made several attempts to prove what is asked in the image below. I need to use the Sherman-Morrison formula to check that the inverse of the H_{k+1} matrix can be obtained by the last formula.
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https://math.stackexchange.com/questions/2785485/applying-sherman-morrison-woodbury-to-obtain-rank-2-update – whpowell96 Dec 04 '19 at 23:48
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whpowell96 I looked at that post but I still can't finish the proof, Could you please help me? – Bruno Pires Dec 05 '19 at 18:08