Page 303 - 35Linear Algebra
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                                         Least squares and Singular Values






                                                                                    linear
                   Consider the linear algebraic equation L(x) = v, where L: U −−−→ W and
                   v ∈ W are known while x is unknown. As we have seen, this system may
                   have one solution, no solutions, or infinitely many solutions. But if v is not
                   in the range of L there will never be any solutions for L(x) = v.






















                   However, for many applications we do not need an exact solution of the
                   system; instead, we may only need the best approximation possible.


                         “My work always tried to unite the Truth with the Beautiful,
                         but when I had to choose one or the other, I usually chose the
                         Beautiful.”
                                                                – Hermann Weyl.


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