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(N) The mapping ||x||(--) := V(x|x) : X → R is a norm on X. CS) |(x\y)| < ||||(1) ||y||41» (x, y € X ). (P) |r + y|l?1) = ||"|) + |1y||/1) + 2R(x|y) (x, y E X ). |(-) (-|-)

(N) The mapping ||x||(--) := V(x|x) : X → R is a norm on X. CS) |(x\y)| < ||||(1) ||y||41» (x, y € X ). (P) |r + y|l?1) = ||"|) + |1y||/1) + 2R(x|y) (x, y E X ). |(-) (-|-)

Advanced Engineering Mathematics
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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(CS) is called the Cauchy-Schwarz inequality and (PI) is called the parallelogram identity.

Let X be a vector space over K and let (-|:) : X × X –→ K be a scalar product. The following holds true: (N) The mapping ||x||(-1-) := V(x|x) : X → R is a norm on X. (CS) |(x|y)| < |||G)||4) (x, y € X ). (P) ||r + y|l?1) = ||-, + ||y, + 2R(x|y) (x, y E X ). (PI) ||r + y|l/1) + ||a – y|l21) = 2(||/71) + M,) (r, y E X ).
Transcribed Image Text:Let X be a vector space over K and let (-|:) : X × X –→ K be a scalar product. The following holds true: (N) The mapping ||x||(-1-) := V(x|x) : X → R is a norm on X. (CS) |(x|y)| < |||G)||4) (x, y € X ). (P) ||r + y|l?1) = ||-, + ||y, + 2R(x|y) (x, y E X ). (PI) ||r + y|l/1) + ||a – y|l21) = 2(||/71) + M,) (r, y E X ).
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