Class Notes (839,189)
Canada (511,223)
Mathematics (2,859)
MAT224H1 (138)

Using coordinates, Algebra Transformations, Change of Basis, change of basis for transformation

7 Pages

Course Code
Martin, Burda

This preview shows pages 1 and half of page 2. Sign up to view the full 7 pages of the document.
Tuesday 25012011, Lecture notes by Y. Burda 1 Using coordinates We are going to expand on the idea that while one should think about vectors in vector spaces and linear transformations, computations should be done 1 with coordinates and transformation matrices . Example: Let T : P 2 be t1e dierentiation mapping T(p) = p . Let A = (1 x,1 + x,1 + x + x ), B = (1 x,x) be bases of P a2d P 1 respectively. Find [T] and use it to nd a basis for kerT and ImT. B,A Solution: To nd [T] we should apply T to basis vectors from A and B,A express the results as linear combinations of vectors from B. For the vector 1 x we have [T(1 x)]B= [1] B To nd [1] B we should express 1 as 11 x) + 2 for some 1, 2 R. If 1 = 1(1 x) + 2x, then 1 1, = 21. Thus [T(1 x)] = [1] = 1 B B Similarly we nd [T(1 + x)B = [1]B= ( 1) T(1 + x + x ) = [1 + 2x]B= ( 3 B Hence [T] = 1 1 1 B,A 1 1 3 To nd kerT we recall that v kerT if and only if its coordinates vector x = [v] solves [T] x = 0. A B,A To solve the system [T]B,A x = 0 we row-reduce the matrix 1 1 1 1 1 3 1 And remember: hours of calculations can often spare you tens of minutes of thinking! 1
More Less
Unlock Document

Only pages 1 and half of page 2 are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.