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

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phi
 3 years ago
Best ResponseYou've already chosen the best response.2I 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

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

phi
 3 years ago
Best ResponseYou've already chosen the best response.2use 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

phi
 3 years ago
Best ResponseYou've already chosen the best response.2write 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: \[ 4 (a \cdot b)^2 4 a^2 b^2 ≤ 0 \]

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

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