Cauchy-Schwarz-Bunyakovski inequality |
Cauchy-Schwarz inequality |
Cauchy's inequality
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Definicja
wiek 16 lat poziom 3
| ( a1 b1 + a2 b2 + ... + an bn ) 2 ≤ + ( a1 2 + a2 2 + ... + an 2 ) ( b1 2 + b2 2 + ... + bn 2 ) |
|
for two sets of real numbers a
i, b
i. Equality occurs if [(
a1)/(
b1)] = [(
a2)/(
b2)] = ... = [(
an)/(
bn)] .
Definicja
wiek 19 lat poziom 4
Given an inner product x,y → (x,y) , we have
This is proved by considering the (non-real) roots of the quadratic equation |x+re
i θy |
2=0 for suitable θ .
Ufundowana przez: EU Socrates Minerva, HeyMath!, Cambridge University Press