I am confused about a proof of the Schwarz inequality in my book...(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

[tex]\left(\sum_{j=1}^n |a_j \overline{b}_j |\right)^2\leq \left(\sum_{j=1}^n |a_j|^2\right) \left(\sum_{j=1}^n |b_j|^2\right).[/tex]

3. The attempt at a solution

In the proof in my book (Rudin) it sets [tex]A = \sum a_j^2[/tex] and [tex]B = \sum b_j^2[/tex] and [tex]C = \sum a_j \overline{b}_j[/tex]. It assumesB > 0and then says

[tex]\sum {|Ba_j - Cb_j|}^2 = B^2 \sum {|a_j|}^2 - B \overline{C} \sum a_j \overline{b}_j - BC \sum \overline{a}_j b_j + |C|^2 \sum |b_j|^2 = B^2 A - B |C| ^2 [/tex]

I don't understand how it got between those two steps.

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# Homework Help: Question about the Schwarz inequality

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