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From: eric g on 24 Apr 2010 03:58
Hello Group,
What is the difference of those when solving the problem A.x=b?
What are the difference scenarios of one vs. the other?
best regards,
Eric

From: carlos on 25 Apr 2010 06:25
On Apr 24, 1:58 am, eric g <eric.p...(a)gmail.com> wrote:
> Hello Group,
> What is the difference of those when solving the problem A.x=b?
> What are the difference scenarios of one vs. the other?
> best regards,
> Eric

The distinctions are difficult to state unless one introduces the
generalized inverse in full generality. For example, a vector x is a
LS
(least squares) solution of A x = b if and only if

x = A{1,3} b + (I-A{1,3}) y y=arbitrary vector (*)

where A{1,3} is a generalized inverse of A that satisfies Penrose's
conditions 1 and 3. The pseudoinverse A{1,2,3,4} satisfies conditions
1 thru 4 so it is a particular case of (*) For details see the
book of
Ben-Israel and Greville, 2nd ed, Chapters 2-3. (In that book the
pseudoinverse is called the Moore-Penrose inverse)

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