Show that the function (V1, V₂) = 2w1W2 + x1x2 - Y1Y2 +2122 defined for any vectors V₁ = (x1, y1, 21, W₁) and v₂ = (x2, Y2, 22, W2) in vector space R4 is not an inner product. Hint. Indicate which axiom(s) of inner product space is (are) not satisfied and give an example of the vector(s) which do(es) not satisfy the axiom(s).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Show that the function
(V1, V2) = 2w₁ W2 + X1 X2 - Y1Y2 + Z122
defined for any vectors V₁ = (x1, y₁, 2₁,w₁) and v₂ = (x2, Y2, 22, w₂) in vector space R4 is not an
inner product.
Hint. Indicate which axiom(s) of inner product space is (are) not satisfied and give an example
of the vector(s) which do(es) not satisfy the axiom(s).
Transcribed Image Text:Show that the function (V1, V2) = 2w₁ W2 + X1 X2 - Y1Y2 + Z122 defined for any vectors V₁ = (x1, y₁, 2₁,w₁) and v₂ = (x2, Y2, 22, w₂) in vector space R4 is not an inner product. Hint. Indicate which axiom(s) of inner product space is (are) not satisfied and give an example of the vector(s) which do(es) not satisfy the axiom(s).
Expert Solution
Step 1: Example

Advanced Math homework question answer, step 1, image 1

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,