Purchase Solution

Normal matrices

Not what you're looking for?

Ask Custom Question

Show that each matrix type is normal.

1. Hermitian
2. skew-Hermitian
3. unitary
4. symmetric
5. skew-symmetric
6. orthogonal

Purchase this Solution

Solution Summary

This shows how to prove that each matrix type is normal.

Solution Preview

I will use the notation:
A^T = transpose(A)
A^* = complex_conjugate(A)
A^t = (A^T)^* = hermitian_conjugate(A)
A^i = inverse(A)
A matrix, A, is defined to normal if and only if
[A , A^t] = A A^t - A^t A = 0
(comment: A matrix, A, is also normal if and only if there exists a unitary matrix, U, such that (U A U^t) is ...

Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

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

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