This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MA 35100 LECTURE NOTES: MONDAY, FEBRUARY 8 Matrices which Commute We recap the main results from the previous lecture. Let A be an q m matrix and B be an n p matrix. a. The product B A is defined only when the number of rows of A (namely q ) is equal to the number of columns of B (namely q ). b. If p = q , then the n m matrix C = B A is defined as the matrix of the linear transformation T ( ~x ) = B ( A~x ). c. If the columns of A and ~v j , then the columns of B A and B~v j . Explicitly, B A = B    ~v 1 ~v 2 ~v m    =    B~v 1 B~v 2 B~v m    . As an example, we showed that 6 7 8 9 1 2 3 5 = 27 47 35 61 and 1 2 3 5 6 7 8 9 = 22 25 58 66 . This proves the following fact: Theorem. Matrix multiplication is noncommutative. Explicitly, let A and B be n n matrices. Then AB and B A are both defined, but in general AB 6 = B A ....
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 UniversityWest Lafayette.
 Spring '10
 EGoins
 Linear Algebra, Algebra, Matrices

Click to edit the document details