lecture_9 - MA 35100 LECTURE NOTES: MONDAY, FEBRUARY 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 35100 LECTURE NOTES: MONDAY, FEBRUARY 1 Geometric Interpretation of Matrix Multiplication Given a 2-dimensional vector ~x R 2 and a 2 2 matrix A , the product T ( ~x ) = A~x gives a new 2-dimensional vector ~ y = T ( ~x ). We discuss some examples to consider how linear transformations transform the plane R 2 . Denote the following three 2-dimensional vectors ~u = 1 , ~v = , and ~w = 2 . We will consider several types of transformations. To begin, consider the linear transformation T : R 2 R 2 defined by T ( ~x ) =- 1 1 ~x that is T x 1 x 2 =- 1 1 x 1 x 2 =- x 2 x 1 . The three 2-dimensional vectors transform to T ( ~u ) = 1 , T ( ~v ) = , and T ( ~w ) =- 2 . Hence T is a rotation by 90 in the counterclockwise direction. With this example in mind, consider now the following six matrices: A = 2 0 0 2 B = 1 0 0 0 C =- 1 0 0 1 D = 0 1- 1 0 E = 1 0 . 5 1 F = 1- 1 1 1 Multiplication by A is a scaling by a factor of 2: A~u = 2 , A~v = , and A ~w = 4 . Multiplication by B is a projection onto the horizontal axis : B ~u = 1 , B~v = , and B ~w = ....
View Full Document

This note was uploaded on 10/18/2010 for the course MATH 351 taught by Professor Egoins during the Spring '10 term at Purdue University-West Lafayette.

Page1 / 3

lecture_9 - MA 35100 LECTURE NOTES: MONDAY, FEBRUARY 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online