More specifically if there is a matrix whose two rows are exactly identically, its inverse can't be calculated because its determinant is 0. However, its pseudo-inverse can still be found out. Is there any significance of the pseudo inverse of such a matrix?
2026-03-26 22:57:57.1774565877
What does the pseudo of a non-invertible matrix signify?
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Short: Yes.
Long: Given the least-squares problem $$\bar x = \mathop{\rm arg\;min}_{x\in\mathbb R^n} \|Ax-b\|_2$$ A solution is $$\bar x = A^\dagger b$$ Where $A^\dagger = (A^TA)^{-1} A^T$ is the pseudoinverse of $A$. Moreover all solutions are characterised by $\bar x + z$ where $Az = 0$ i.e. $z\in\ker A$.