Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
5. Let V be a finite dimensional vector space over F. Let T = L(V) be an operator such that T* = -T (these operators are sometimes called skew-adjoint). Prove that if A is an eigenvalue of T, then λ = 0 + bi for some bЄ R (i.e., A has no real part).

5. Let V be a finite dimensional vector space over F. Let T = L(V) be an operator such that T* = -T (these operators are sometimes called skew-adjoint). Prove that if A is an eigenvalue of T, then λ = 0 + bi for some bЄ R (i.e., A has no real part).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 60E: Define T:R2R2 by T(v)=projuv Where u is a fixed vector in R2. Show that the eigenvalues of A the...
See similar textbooks
icon
Related questions
Question
5. Let V be a finite dimensional vector space over F. Let T = L(V) be an operator such that T* = -T (these operators are sometimes called skew-adjoint). Prove that if A is an eigenvalue of T, then λ = 0 + bi for some bЄ R (i.e., A has no real part).
Transcribed Image Text:5. Let V be a finite dimensional vector space over F. Let T = L(V) be an operator such that T* = -T (these operators are sometimes called skew-adjoint). Prove that if A is an eigenvalue of T, then λ = 0 + bi for some bЄ R (i.e., A has no real part).
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
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS