Class Notes (836,414)
United States (324,504)
Mathematics (396)
MATH 2331 (7)
Lecture

# Linear Transformations

2 Pages
53 Views

School
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
Me

OR

Join OneClass

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

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.