# Finding the Standard Matrix

• Nov 22nd 2010, 11:13 PM
Lprdgecko
Finding the Standard Matrix
Could someone please explain how to find the standard matrix? I have a test tomorrow and my professor wasn't very clear about this part, and the textbook isn't helping much, either. Here are a couple of practice problems my professor gave us:

Assume T is a linear transformation. Find the standard matrix of T.

(1.) T: R^2 --> R^2 rotates points (about the origin) through -(pi)/4 radians (clockwise)

(2.) T: R^2 --> R^2 is a vertical shear transformation that maps e1 into (e1 - 2(e2)) but leaves vector e2 unchanged.

Any help would be greatly appreciated.
• Nov 23rd 2010, 02:24 AM
Lprdgecko
Nevermind - I know how to do it now. I do have one question though. What does "vertical shear transformation" mean? Because it didn't really change the way I worked the problem.
• Nov 23rd 2010, 04:39 AM
HallsofIvy
The problem itself pretty much tells you what it is: T maps "e1 into (e1 - 2(e2)) but leaves vector e2 unchanged"- a "shear" stretches vectors along one axis.