Class Notes (806,874)
Canada (492,493)
Mathematics (2,710)
MAT224H1 (115)

Fields, Vector Spaces and Vector Subspaces

4 Pages
Unlock Document

University of Toronto St. George
Martin, Burda

Tuesday 1101, lecture notes by Y. Burda 1 Fields To do linear algebra we only need to do arithmetic operations to numbers. So instead of numbers we can work with anything we can add, multiply, subtract and divide (with the usual properties of the operations being assumed). 2 1 Example: the inverse of a matrix 3 4 cant be 3 1 because nding 2 2 inverse matrix involves only arithmetic operations, the entries of the matrix we started with are rational and thus the answer should be a matrix with rational entries only. The relevant denition here is that of a eld: A set K with operation + and is called a eld if: Sum of two numbers is a number x + y K for all x,y K Order doesnt matter for addition x + y = y + x for all x,y K Grouping doesnt matter for addition (x+y)+z=x+(y+z) for all x,y,z K Zero is a number there exists element 0 K such that x + 0 = x for all x K One can subtract numbers for any x K there exists x K such that x + (x) = 0 Product of numbers is a number xy K for all x,y K Order doesnt matter for multiplication xy = yx for all x,y K Grouping doesnt matter for products (xy)z = x(yz) for all x,y,z K One is in the eld There exists 1 K such that 1x = x for all x K 1
More Less

Related notes for MAT224H1

Log In


Don't have an account?

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.