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Misc Math / Orthogonal systems: approximation
« on: October 20, 2012, 06:29:47 PM »
Hi all,
First, I have a trivial question on the definition of the {u_n}(finite orthonormal system) that's mentioned at the introduction of this section in lecture note #14.
Is this set/system defined in H, in which you did not mention whether it's infinite or finite? or does it span its own space(any) based on perhaps infinite/finite number of linear hulls including K, which in particular belongs to H?
Also In the following Theorem 1
b) I think this implies w is linear independent of other elements in K, regardless of "unique" in a) or c)
c) do you mean "w in K"(summation of alpha times u_n) rather than equal to it?
Thanks in advance.
First, I have a trivial question on the definition of the {u_n}(finite orthonormal system) that's mentioned at the introduction of this section in lecture note #14.
Is this set/system defined in H, in which you did not mention whether it's infinite or finite? or does it span its own space(any) based on perhaps infinite/finite number of linear hulls including K, which in particular belongs to H?
Also In the following Theorem 1
b) I think this implies w is linear independent of other elements in K, regardless of "unique" in a) or c)
c) do you mean "w in K"(summation of alpha times u_n) rather than equal to it?
Thanks in advance.