# What does $c.c.$ mean in this proof?

This is a proof from Wikipedia of Moore-Penrose inverse being the optimal solution of a least squares problem, in which there is a acronym $c.c.$ occurred in some of the equations. Mind if I ask what does that represent?

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Complex Conjugate –  Pragabhava Oct 3 '12 at 6:17

It means complex conjugate (of the term preceeding it), but in my opinion it is very lazy notation, for example, line 1 reads \begin{align*} \|Ax-b\|^2 & = \|Az - b + Ax - Az\|^2\\ &= \|Az - b\|^2 + (Az - b)^*(Ax - Az) + \overline{(Az - b)^*(Ax - Az)} + \|A(x - z)\|^2 \end{align*}

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It might be lazy in this case, but if you are doing some nasty algebra, it's very convenient. See Olver's Asymptotics and Special Functions chapter on Liouville-Green transform and see what I mean :) –  Pragabhava Oct 3 '12 at 6:22
Might be. I don't have a copy at hand, but I prefer $2\Re z$ over $z + \text{c.c.}$. –  martini Oct 3 '12 at 6:24
It's just a matter of style I guess. I'd use the c.c. notation to imply that not much attention should be payed to that term, as is just the complex conjugate. I can say that -for me- this is not the case. –  Pragabhava Oct 3 '12 at 6:29