Page 303 - 35Linear Algebra
P. 303
17
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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