For x = (x₁,...,xn), y = (y₁,..., yn) R", define (x, y) = -1 j²xjYj. (a) Show that (,) is an inner product on R". (b) Suppose that n = -2, and draw the unit ball B = {x € R² : ||x|| ≤ 1} (where || || is the norm derived in the usual way from the inner product (,)).

For x = (x₁,...,xn), y = (y₁,..., yn) R", define (x, y) = -1 j²xjYj. (a) Show that (,) is an inner product on R". (b) Suppose that n = -2, and draw the unit ball B = {x € R² : ||x|| ≤ 1} (where || || is the norm derived in the usual way from the inner product (,)).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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For x = (x₁,...,xn), y = (y₁,..., yn) R", define (x, y) = -1 j²xjYj.
(a) Show that (,) is an inner product on R".
(b) Suppose that n = -2, and draw the unit ball B = {x € R² :
||x|| ≤ 1} (where || || is the norm derived in the usual way from
the inner product (,)).

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Step 1: Inner Product

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Step 2: Verification of properties of inner product

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Step 3: Verification of properties of inner product

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Step 4: Drawing unit ball

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