Linear Transformations

2 Pages
53 Views
Unlock Document

Department
Mathematics
Course
MATH 2331
Professor
Rita Jimenez Rolland
Semester
Spring

Description
Linear Algebra Notes Linear Transformations February 6, 2014 ▯ ▯ ▯ ▯ ▯ ▯ 0 1 2 Example. Write the vector as a linear combination of the vectors and . ▯ ▯ ▯ ▯ ▯ ▯ 0 1 ▯1 0 1 2 = 0 + 0 0 1 ▯1 ▯ ▯▯ ▯ ▯ ▯ 1 2 x1 0 h . i matrix notation:x = b ! = ; augmented matrixA . b 1 ▯1 x2 0 Linear Transformations f : R ! R ▯ f(x) = x;f(x) = x + 2x + 1;f(x) = e ;::: m n we want to look at functions f! RR ▯ ▯ ▯ ▯ x1 y1 position on the plane: ! position after an hour: ▯ ▯ ▯ ▯2 ▯ ▯ y2 x 3x + 4x y f 1 = 1 2 = 1 x2 x1▯ x2 y2 (3x1+ 4x2and x1▯ x2are both linear functions!) A function T from R to Rn is called a linear transformation if 9 a matrix A of size n ▯ m such that T(x) = An▯mx 8 x 2 R ▯ ▯ 3 4 F(x) = 1 ▯1 x =y~ 0 1 0 10 1 0 1 x a a ▯▯▯ a x y 1 11 12 1m 1 1 B x2 C B a21 a22 ▯▯▯ a2mCB x2C B y2C T(x) : B . C = B . . .. . CB . C = B . C @ . A @ . . . . [email protected] . A @ . A x
More Less

Related notes for MATH 2331

Log In


OR

Join OneClass

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

Sign up

Join to view


OR

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.


Submit