u= (₁, ₂), v = (v₁, v₂) € C². Show that (u, v) = 2u1v1 +3u₂v2 defines an inner product on C². Explain why |2u₁₁+3u₂v₂ ≤ (2|u₁|² +3|u₂|²) (2|v₁|² +3|v₂|²) 1.
u= (₁, ₂), v = (v₁, v₂) € C². Show that (u, v) = 2u1v1 +3u₂v2 defines an inner product on C². Explain why |2u₁₁+3u₂v₂ ≤ (2|u₁|² +3|u₂|²) (2|v₁|² +3|v₂|²) 1.
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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![V. Let u = (U₁, U₂), v = (v₁, v¹₂) € C².
1. Show that (u, v) = 2u₁v₁ + 3u₂v₂ defines an inner product on C².
2. Explain why |2u₁ +3₂V₂] ≤ (2|u₁|² +3|u₂|²) (2|v₁|² +3|v₂|²) } .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1be657f-6b04-4fb6-883d-75c0198282db%2F34ba6762-59e9-42ad-b3e6-299c317938e5%2Fau77h3w_processed.png&w=3840&q=75)
Transcribed Image Text:V. Let u = (U₁, U₂), v = (v₁, v¹₂) € C².
1. Show that (u, v) = 2u₁v₁ + 3u₂v₂ defines an inner product on C².
2. Explain why |2u₁ +3₂V₂] ≤ (2|u₁|² +3|u₂|²) (2|v₁|² +3|v₂|²) } .
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