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Mathematics-Online course: Linear Algebra - Normal Forms - Singular Value Decomposition

Moore-Penrose Conditions


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The pseudo inverse (Moore-Penrose inverse) $ A^+$ of an $ m\times n$-matrix $ A$ is uniquely determined by the following identities:
  1. $\displaystyle A A^+ A = A
$

  2. $\displaystyle A^+ A A^+ = A^+
$

  3. $\displaystyle (A A^+)^{\operatorname t}= A A^+
$

  4. $\displaystyle (A^+ A)^{\operatorname t}= A^+ A\,.
$

(Authors: App/Burkhardt/Höllig)

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  automatically generated 4/21/2005