Assignments

# Assignments - ± a b c d ² is a root of its characteristic...

This preview shows page 1. Sign up to view the full content.

Math 235 Assignment 10 Not To Be Submitted 1. Let A be skew-Hermitian. Prove that all the eigenvalues of A are purely imaginary. 2. Let A be normal and invertible. Prove that B = A * A - 1 is unitary. 3. Unitarily diagonalize the following matrices. a) A = a b - b a b) B = 4 i 1 + 3 i - 1 + 3 i i c) C = 1 0 1 + i 0 2 0 1 - i 0 0 . 4. By direct computation, show that A =
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ± a b c d ² is a root of its characteristic polynomial. 5. Prove that if a matrix is unitary, Hermitian, or skew-Hermitian, then it is normal. Find a normal matrix that is not unitary, Hermitian or skew-Hermitian. 6. If A 2 = A , show that rank A = tr A . 1...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern