Assume that there exists a matrix $A∈R^{m×n}(m≠n)$ whose generalized inverse matrix is $X$, and $X$ satifies the formula: $$ A=AXA\\ (XA)^T=XA $$ How to calculate the generalized inverse matrix Y of $B=[A,a](a∈R^{m×t},m\neq t)$,which also satifies the formula(the matrix $A$, the matrix $a$, the generalized inverse matrix of $A$ have been known): $$ B=BYB\\ (YB)^T=YB $$
2026-03-18 03:36:51.1773805011
How to calculate the generalized inverse of a matrix on new columns
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