Homework Help is Here – Start Your Trial Now!
Math
Algebra
2. Let (X,(x) and (Y, (,)) be Hilbert spaces. For (x1,y1), (2, y2) = X x Y, put ((x1,y1), (2, 2))xxy = (x1, x2)x + (y1, y2)Y. Show that (xxy is an inner product on the direct sum X x Y and it is a Hilbert space under this inner product.

2. Let (X,(x) and (Y, (,)) be Hilbert spaces. For (x1,y1), (2, y2) = X x Y, put ((x1,y1), (2, 2))xxy = (x1, x2)x + (y1, y2)Y. Show that (xxy is an inner product on the direct sum X x Y and it is a Hilbert space under this inner product.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
See similar textbooks
icon
Related questions
Question
2. Let (X,(x) and (Y, (,)) be Hilbert spaces. For (x1,y1), (2, y2) = X x Y, put ((x1,y1), (2, 2))xxy = (x1, x2)x + (y1, y2)Y. Show that (xxy is an inner product on the direct sum X x Y and it is a Hilbert space under this inner product.
Transcribed Image Text:2. Let (X,(x) and (Y, (,)) be Hilbert spaces. For (x1,y1), (2, y2) = X x Y, put ((x1,y1), (2, 2))xxy = (x1, x2)x + (y1, y2)Y. Show that (xxy is an inner product on the direct sum X x Y and it is a Hilbert space under this inner product.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS