When data from a table (or tables) needs to be manipulated, easier to deal with info in form of a matrix.

Matrices

Fresh Soph Jun Sen

A 0 3 4 2

B 0 4 4 7

C 2 1 0 6

D 1 3 2 2

F 1 2 1 0

Terminology

Entry: The individual pieces of data in the matrix are called entries.

The entry in the ith row and jth column is:

The diagonal entries occur when i = j.

From previous matrix:

Order: If a matrix has m rows and n columns, then the matrix has an order of

Special Matrices

Identity: A square matrix with 1 for each diagonal entry and 0 for each non-diagonal entry. (written as I)

Square: A matrix with m=n.

Zero: A matrix with all entries = 0.

Special Matrices – continued

Row: A matrix of order 1 by n, also called a row vector.

Column: A matrix of order m by 1, also called a column vector.

Operations

Multiply a matrix by a non-zero constant.

531

012

032

A

Add two matrices of the same order.

Subtract two matrices of the same order.

101

617

520

B

16

15

14

C

BA BA C2

Balance of trade: A-B, exports - imports

A: US oil and coal exports to Canada, Germany, and France

B: US oil and coal imports from Canada, Germany, and France

Example 1

720

63.42

107.27

A

1317

8310

15.2

B

Power to influence: in a flow of information, who is the key?

otherwise

j odirectly t toinfo sends i if

0

1

ija

Create two matrices, A and B, with the following entries:

Example 2

otherwise

betweengo 1most at with j toinfo sends i if

0

1

ijb

1 2

3

4

5

otherwise

j odirectly t info sends i if

0

1

ija

Compute A+B. The row sum that is greatest in matrix A+B corresponds to person with most influence.

Example 2 – continued

otherwise

between-go 1most at with j toinfo sends i if

0

1

ijb

1 2

3

4

5