(b1, b2, ..., bn) be any two vectors in R". The inner product Let a = (a1, a2, . .. , an) and b = (dot product) of these two vectors are defined as ā ·b = a1b1 + a2b2 + · · · + anbn; and also the norms of these vectors are defined as |Jā|| = Vā a = V až + a3 + |||| = V5.5 = V/bỉ + b3 + • · + an, + b%. n Prove the Cauchy-Schwarz inequality (a b)? < ||ā||2||P', that is the inequality (abı + azb2 + · ..+ anbn)² < (a? + a3 + · ..+ a (bỉ + b3 + + a)(bỉ + b3 + + b% ). ..

(b1, b2, ..., bn) be any two vectors in R". The inner product Let a = (a1, a2, . .. , an) and b = (dot product) of these two vectors are defined as ā ·b = a1b1 + a2b2 + · · · + anbn; and also the norms of these vectors are defined as |Jā|| = Vā a = V až + a3 + |||| = V5.5 = V/bỉ + b3 + • · + an, + b%. n Prove the Cauchy-Schwarz inequality (a b)? < ||ā||2||P', that is the inequality (abı + azb2 + · ..+ anbn)² < (a? + a3 + · ..+ a (bỉ + b3 + + a)(bỉ + b3 + + b% ). ..

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(b1, b2, ..., bn) be any two vectors in R". The inner product
Let a = (a1, a2, . .. , an) and b =
(dot product) of these two vectors are defined as
ā ·b = a1b1 + a2b2 + · · ·
+ anbn;
and also the norms of these vectors are defined as
|Jā|| = Vā a = V
až + a3 +
|||| = V5.5 = V/bỉ + b3 + • ·
+ an,
+ b%.
n
Prove the Cauchy-Schwarz inequality (a b)? < ||ā||2||P', that is the inequality
(abı + azb2 +
· ..+ anbn)² < (a? + a3 + · ..+ a (bỉ + b3 +
+ a)(bỉ + b3 +
+ b% ).
..

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