I’ve never seen these applied to a problem other than when one wants to increase the dimension of the matrix by one or vice versa… very eye opening. Will look for applications in my own work now.
Also appreciated the derivation of sorts of the formula, starting with the case where the main matrix is the identity.
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Ah, the good ol' Sherman–Morrison formula. (https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formu...) Really useful to know sometimes.
A more general formula is known as the Woodbury matrix identity (https://en.wikipedia.org/wiki/Woodbury_matrix_identity), which comes up quite a lot in numerical algorithms.
I’ve never seen these applied to a problem other than when one wants to increase the dimension of the matrix by one or vice versa… very eye opening. Will look for applications in my own work now.
Also appreciated the derivation of sorts of the formula, starting with the case where the main matrix is the identity.