Suppose that A is tall and full column rank
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Suppose that A is tall and full column rank

Singular Value Decomposition 

For a matrix  with SVD,


• Suppose that A is tall and full column rank. Show that x =  is the least squares solution to y = Ax. 

• Suppose that A is fat and full row rank. Show that x =  is the minimum norm solution to y = Ax. 

• Use the singular value decomposition (you should use computing software) to compute an orthonormal basis for 


Hint
In mathematics, an orthonormal basis for an internal product space V with predetermined dimension refers to a basis for V whose vectors are all unit vectors. The essential thing about orthogonal vectors is that a group of orthogonal vectors of cardinality is the same as the dimension of space...

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