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

experimentX Group TitleBest ResponseYou've already chosen the best response.0
I'm particularly looking for something to write in exam
 one year 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
 one year 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: \[ 4 (a \cdot b)^2 4 a^2 b^2 ≤ 0 \]
 one year ago

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

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

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