I am wondering what is the relation between Pseudo-inverses and the following:
$Ax=b$, when $A$ is singular, then $x = \left( A^T A \right)^{-1} \left(A^T b \right)$.
Then, what is the difference between $\left(A^T A\right)^{-1} A^T$ and $A^+$?
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@algae, would like to know what's the syntax of typing math formula properly? I fail to find the relevant link yet... – Wong May 14 '20 at 07:10
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https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse#Linearly_independent_columns – Jean-Claude Arbaut May 14 '20 at 07:10
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But keep in mind that the formula you use is only valid when the columns of $A$ are linearly independent, which is certainly not true if $A$ is square and singular. And you can't write either that $x=\dots$: It's not an inverse. – Jean-Claude Arbaut May 14 '20 at 07:13
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@HingWong You can typeset equations using LaTeX. If you edit your own post (this post), you will see what it looks like. For more information check out this. – algae May 14 '20 at 07:14
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@algae, thx so much! it helps! :) – Wong May 14 '20 at 08:27
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@Jean-Claude Arbaut, oh i see i see! Thx!! – Wong May 15 '20 at 05:59