Vector spaces can be defined where the sets of scalars are different from R and C. For example, we could use Q as the scalars, or Zp, the integers modulo a prime p. What would happen if we tried to define an inner product space for a vector space with scalars in Q or in Z„? Are there any problems with the inner product space conditions in either case?
Vector spaces can be defined where the sets of scalars are different from R and C. For example, we could use Q as the scalars, or Zp, the integers modulo a prime p. What would happen if we tried to define an inner product space for a vector space with scalars in Q or in Z„? Are there any problems with the inner product space conditions in either case?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please explain and elaborate as much as possible. You can answer is in whatever way you want (ex. paragraph), and feel free to make examples to prove the points. The flow should be logical and concise. I'll leave a like for sure. Thank you.
Transcribed Image Text:Vector spaces can be defined where the sets of scalars are different from R and C. For example, we could
use Q as the scalars, or Z,, the integers modulo a prime p. What would happen if we tried to define
an inner product space for a vector space with scalars in Q or in Zp? Are there any problems with the
inner product space conditions in either case?
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