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Unformatted text preview: 12 25 IX.4 presentations) Continuous Limit Laws Marni Remark. What is b − Av for a given Sophie
vector v ∈ Rn ?
Gaussian limit laws Asst #3 Due
If Ax = b was consistent, and v is a solution, then b − Av = 0.
14 Dec 10 Presentations So b − Av is a vector that represents how different from a solution to this
system v is: if b − Av = (e1 , . . . , en ), then ei is a scalar that represents how
the ith component of Av is far from the ith component of b, which is why it is
called the error vector.
This is why we try to ﬁnd a vector x that minimizes the length of this error
vector, which is exactly e1 + · · · + e2 .
n Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY
Version of: 11-Dec-09 Theorem (7.8.3(a,b)). (a) The least-squares solutions of a linear system
Ax = b are exactly the solutions of the linear system AT Ax = AT b.
If A has full column rank, the normal equation has a unique solution given
by x = (AT A)−1 AT b.
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