linear algebra proof question please show clear thanks Let V be an inner product space over F. If F = R, prove that(u, v) = ||1u + v||²³ − ||1u — v||²2.If F = C, prove that(u, v)1== || u + v||²³ + ² ||u + iv||² − −| ||u — v|| ² — — ||u — iv||²2.--(2)(3)Equations (2) and (3) are called the polarization identities, and they show howthe inner product on V can be recovered from the norm.

Answered: Image /qna-images/answer/46e6f172-cdef-440f-a55b-fbfbf5e40b50.jpg

Answered: Let V be an inner product space over F.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

linear algebra proof question

please show clear thanks

Let V be an inner product space over F. If F = R, prove that
(u, v) = ||1u + v||²³ − ||1u — v||²2.
If F = C, prove that
(u, v)
1
=
= || u + v||²³ + ² ||u + iv||² − −| ||u — v|| ² — — ||u — iv||²2.
-
-
(2)
(3)
Equations (2) and (3) are called the polarization identities, and they show how
the inner product on V can be recovered from the norm.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution