Suppose I have a matrix $A$. Let $A'$ be the transpose of A. Is there any guarantee that $A'A$ has an inverse?
You can find this formula at Adaptive Neuro-Fuzzy Inference System (ANFIS) theory in "LSE Recursive" part. Thank you.
2026-04-04 07:01:40.1775286100
Guarantee of matrix inverse for $A'A$
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I will write $A^TA$ instead of $A'A$. The matrix $A^TA$ has inverse if and only if the columns of $A$ are linearly independent. Indeed, such a matrix is the Gram matrix of the columns of $A$.