MathAlgebraLinear algebraMatrix decomposition

Pseudoinverse

Recognize the pseudoinverse

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Consider an $m \times n$ matrix $A$ of rank $r$ with SVD given by:

$A = \sum_{j=1}^r \sigma_j \ \mathbf{u}_j \, \mathbf{v}_j^T$ What does its pseudoinverse $A^{\dag}$ look like?

Select one option from the list

A^{\dag} = \sum_{j=1}^r \sigma_j^r \ \mathbf{u}_j \, \mathbf{u}_j^T

A^{\dag} = \sum_{j=1}^r \sigma_j \ \mathbf{v}_j \, \mathbf{u}_j^T

A^{\dag} = \sum_{j=1}^r \frac{1}{\sigma_j} \ \mathbf{v}_j \, \mathbf{u}_j^T

A^{\dag} = \sum_{j=1}^r \frac{1}{\sigma_j} \ \mathbf{u}_j \, \mathbf{v}_j^T

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