Question: Let A be an m x n matrix. A kinda-inverse of A is a n x m matrix K such that AKA = A.

Let A be an m x n matrix. A kinda-inverse of A

Let A be an m x n matrix. A kinda-inverse of A is a n x m matrix K such that AKA = A. 1. State the definition of a kinda-inverse in terms of linear maps, without reference to matrices. 2. Show that any matrix has a kinda-inverse. A kinda-inverse K is called symmetric when it also satisfies KAK = K. 3. Prove that any matrix has a symmetric kinda-inverse.

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