Generalized Inverse of a Matrix 1. AA+A = A. 2. A+AA+ = A+ 3. AA+ = (AA+)T, i.e., the matrix AA+ is symmetric. 4. A+A = (A+A)T, i.e., the matrix A+A is symmetric. We shall call these conditions, taken in the order specified above, the MP conditions.
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The first condition states that $AA^+A = A$. This means that when we multiply the matrix $A$ by its generalized inverse $A^+$ and then multiply the result by $A$ again, we get back the original matrix $A$. Show more…
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