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Difficulty: Medium
Category: Linear Algebra & Machine Learning
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Topics: linear-algebra, matrix, pseudoinverse, moore-penrose, rank
Consider a real-valued matrix $A$ of size $m imes n$. The Moore-Penrose pseudoinverse, denoted as $A^+$, is a generalization of the matrix inverse. It exists even if $A$ is not square or does not have full rank. Under what conditions is $A^+ A$ equal to the identity matrix $I_n$?
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