How is the svd defined for a rectangular matrix whose, Basic Computer Science

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How is the svd defined for a rectangular matrix whose

1. How is the SVD defined for a rectangular matrix whose number of rows is smaller than its number of columns?

2. When should the SVD be used for solving a least squares problem? When should it not be used?

3. What is the connection between singular values and the 2-norm of a matrix?

4. What is the connection between singular values and the spectral condition number, κ₂(A)?

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