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p827aps1sola

# p827aps1sola - a b | Z a with A Z | W a = 0 In this Form we...

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Solution to the Second Part of Shankar, Problem 1.3.4 In my original solution, I misinterpreted the phrase “the fnal inequality.” The correct interpretation is that we should show that eq. (1.3.16) becomes an inequality iF and only iF | V a = a | W a , where a is a real and positive scalar. To prove this, we have to show that Re A V | W a = | V || W | iF and only iF | V a = a | W a with a real and positive. Now we can always write | V a = a | W
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Unformatted text preview: a + b | Z a with A Z | W a = 0. In this Form, we have A W | V a = a A W | W a = a | W | 2 , (1) so Re A W | V a = Re A V | W a = (Re a ) | W | 2 . Also | V || W | = r | a | 2 | W | 2 + | b | 2 | Z | 2 ( | W | ) . (2) ±rom this, we can see that | V || W | = Re A W | V a only iF | b | = 0 and also iF Re a = | a | , i. e., iF a is real and positive. Q. E. D. 1...
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