# Questions tagged [pseudoinverse]

The operator which best approximates a solution to a linear system with a singular (non-invertible) matrix.: e.g., the Moore-Penrose pseudoinverse. Use when a question concerns a matrix that is probably singular.

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### Pseudoinverse of a matrix?

In pseudoinverse of a matrix, we have a special case when the columns are linearly independent. It is mentioned in that article and in other articles that It follows that $A^+$ is then a left ...
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### Derivative of the pseudoinverse

Let $K$ be an $n \times m$ matrix with $rank(K)=m$ and consider the pseudoinverse $K^+=(K^TK)^{-1}K^T$. What is the derivative of $K^+$ with respect to some scalar parameter $p$ (Derivative of the ...
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### An example of the Pseudo-inverse of an operator

Let $E$ an infinite dimensional complex Hilbert space and $\mathcal{L}(E)$ be the algebra of all bounded linear operators on $E$. Definition: Let $T \in \mathcal{L}(E)$. The Moore-Penrose inverse of ...
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### Cheap Implementation for the Moore Penrose Pseudoinverse

Can some one explain Adam W's implementation for finding the Moore Penrose Pseudoinverse? http://math.stackexchange.com/questions/75789/what-is-step-by-step-logic-of-pinv-pseudoinverse/317053#317053 ...
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### When does $\ker(M) = Span( I - M^{+}M)$ ? Always?

Let $M$ be an $m \times n$ matrix, where the rows are linearly independent. Let $M^{+}$ be the pseudo-inverse of $M$ (which I think is $M^{+} =M^T\left(MM^T\right)^{-1}$, at least when $m\leq n$). ...
It is well-known that for the general linear system $$\mathbf{X}\mathbf{a}=\mathbf{y}$$ where $\mathbf{X}$ is a rectangular matrix and $\mathbf{a}$ and $\mathbf{y}$ are column vectors of compatible ...