Science:Math Exam Resources/Courses/MATH307/December 2008/Question 10
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 (a) • Q6 (b) • Q7 • Q8 • Q9 • Q10 •
Question 10 

Let A^{H} = A be a skewHermitian complex matrix. Show that the matrix e^{At} is unitary. Note: The superscript H denotes the Hermitian conjugate , which is often also called adjoint matrix or conjugate transpose and written as A^{*} = A^{H}. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

In order for e^{At} to be unitary, we need 
Hint 2 

Use the Maclaurin Expansion 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Calculating the Maclaurin expansion we find that Thus, 