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I have figured out a possible solution and I only need someone to tell me if I'm correct. The solution is the following:

If a matrix has linearly independent columns, then $A^+$ = $(A^TA)^{-1}A^T$

Therefore, by operating: = $A^{-1}(A^T)^{-1}A^T$ = $A^{-1}$ since $(A^T)^{-1}A^T = I$ So $A^+ = A^{-1}$

Am I right with this proof?

Thank you

amWhy
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David Vázquez Masero
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  • How is $A^+$ defined? – Bijesh K.S Jun 11 '17 at 12:50
  • More complete answers are given in the more complete form of your question: https://math.stackexchange.com/questions/2318428/if-a-is-a-non-square-matrix-with-orthonormal-columns-what-is-a/2320169#2320169 – dantopa Jun 12 '17 at 19:47

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If you're allowed to assume that $A^+ = (A^TA)^{-1}A^T$, then your proof is indeed correct.

Ben Grossmann
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