Purchase Solution

Left and Right Eigenvectors with Distinct Eigenvalues

Not what you're looking for?

Ask Custom Question

Let A belonging to C^nxn be a skew-hermitian.
a) Prove directly that the eigenvalues of A are purely imaginary.
b) Prove that if x and y are eigenvalues associated to distinct eigenvalues, then they are orthogonal, i.e. x^H*y = 0

Purchase this Solution

Solution Summary

In this solution, we prove that if A is a complex-valued square matrix with right eigenvector x and corresponding eigenvalue lambda as well as another condition detailed within, then y^H x = 0.

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.