I calculated x^ (residual of x) to be [1.4127; -.0159; .8889]
r(x^) = b-A*x^ = [1.7143; 0.5714; 0; -1.1429]
Nul(A')=[-1.5;-.5;0;1]
so how accurate is MATLAB in calculating least square solution?
#4
hytuoc
26
0
anyone know the answer to my question above?
#5
LeBrad
214
0
Are you asking how does Matlab choose the solution when you give it an overdetermined system?
It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC).
Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?