Quantum Country exercise 6

This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for convenience in referring to them.

Exercise 6. Show that the identity matrix I is unitary.

Answer: Since I is symmetric we have I^T = I and since the values of I are all real we have \left( I^T \right)^* = I^T. We thus have I^\dagger I = \left( I^T \right)^* I = I^T I = II = I by the definition of I.

Since I^\dagger I = I the matrix I is unitary.

This entry was posted in quantum country. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s