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Let V be an inner product space over R. Define a function d: V x V → R by d(u, v) = ||u- vll where u, v E V. This is called the distance from u to v. Prove d(u, v) ≤ d(u, w) + d(u, v) for all u, v, w EV.

Let V be an inner product space over R. Define a function d: V x V → R by d(u, v) = ||u- vll where u, v E V. This is called the distance from u to v. Prove d(u, v) ≤ d(u, w) + d(u, v) for all u, v, w EV.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 67E
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Let V be an inner product space over R. Define a function d : V × V → R by d(u, v) = ||uv|| where u, v E V. This is called the distance from u to v. Prove d(u, v) ≤ d(u, w) + d(u, v) for all u, v, w EV.
Transcribed Image Text:Let V be an inner product space over R. Define a function d : V × V → R by d(u, v) = ||uv|| where u, v E V. This is called the distance from u to v. Prove d(u, v) ≤ d(u, w) + d(u, v) for all u, v, w EV.
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