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experimentX
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if \( a\) and \( b\) are two vectors in linear vector space, prove CauchySwartz inequality \( a.b \geq a.b\)
 2 years ago
 2 years ago
experimentX Group Title
if \( a\) and \( b\) are two vectors in linear vector space, prove CauchySwartz inequality \( a.b \geq a.b\)
 2 years ago
 2 years ago

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phi Group TitleBest ResponseYou've already chosen the best response.2
I have seen a proof that udw:1346599918682:dwses the idea that a quadratic y= a x^2 + bx +c is always positive for all values of x if its discriminate is negative: this means complex roots
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
I'm particularly looking for something to write in exam
 2 years ago

phi Group TitleBest ResponseYou've already chosen the best response.2
use this idea with  a + x b^2 where a and b are vectors and x is a scalar this must always be positive for all values of x
 2 years ago

phi Group TitleBest ResponseYou've already chosen the best response.2
write the magnitude squared as a dot product  a + x b^2 ≥0 \[a^2 + 2(a \cdot b) x + b^2 x^2 ≥ 0\] as noted above, the discriminate of this quadratic in x must be negative to guarantee all values ≥ 0 for all x: \[ 4 (a \cdot b)^2 4 a^2 b^2 ≤ 0 \]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
how do you generalize it to n space?
 2 years ago

phi Group TitleBest ResponseYou've already chosen the best response.2
The vectors a and b are in n space.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
i see..
 2 years ago
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