Intro to Matrices

MatricesMM1 module 3, lecture 1

Slide number 2

Matrices lesson 1 objectives

• After this lesson you should have a clear understanding of:• What matrices are;• Performing basic operations on matrices;• Special forms of matrices

Slide number 3

What is a matrix?

• A matrix is a rectangular array of elements

• The elements may be of any type (e.g. integer, real, complex, logical, or even other matrices).

• In this course we will only consider matrices that have integer or real number values.

5 0 1 23 4 9 23 1 4 2

Slide number 4

Order of matrices…

• Order 4  3:

• Order 3  4:

3 columns

4 rows

5 0 1

2 3 4

9 2 6

3 1 4

4 columns

3 rows

5 0 1 2

3 4 9 2

3 1 4 2

Slide number 5

…Order of matrices

• Order 2  4:

• Order 1  6:

• Order 3  1:

1 columns

3 rows

3

1

5

6 columns1 rows

2 1 1 2 1 5

4 columns2 rows

23 0.5 4.3 12

8 2 8 1

Slide number 6

Specifying matrix elements

• aij denotes the element of the matrix A on the ith row and jth column.

A

column j

row i

5 0 12 3 4 9 2 63 1 4

• a12 = 0

• a21 = 2

• a23 = -4

• a32 = 2

• a41 = 3

• a43 = 4

Slide number 7

Matrix operations: scalar multiplication

• Multiplying an m n matrix by a scalar results in an m n matrix with each of its elements multiplied by the scalar.

• e.g.

826

12418

864

2010

413

629

432

105

2

1239

18627

1296

3015

413

629

432

105

3

Slide number 8

Matrix operations: addition…

• Adding or subtracting an m  n matrix by an m  n matrix results in an m  n matrix with each of its elements added or subtracted.

• e.g.

431

8112

113

136

024

213

541

231

413

629

432

105

417

436

971

334

024

213

541

231

413

629

432

105

Slide number 9

…Matrix operations: addition

• Note that matrices being added or subtracted must be of the same order.

• e.g.

invalid! 113

201

413

629

432

105

Slide number 10

Special matrices: row and column

• A 1  n matrix is called a row matrix.e.g.

• An m  1 matrix is called a column matrix.e.g.

1 columns

3 rows

3

1

5

6 columns1 rows

2 1 1 2 1 5

Slide number 11

Special matrices: square

• An n  n matrix is called a square matrix.i.e. a square matrix has the same number of rows and columns.e.g.

4705

7350

0523

5031

211

010

210

21

321

Slide number 12

Special matrices: distance

• A distance matrix is a square matrix that shows the distances between locations. Distance matrices are frequently used on road maps to show the number of kilometres between major cities. Note that the main diagonal elements are all zeros.

Slide number 13

Matrices lesson 1 objectives

• After this lesson you should have a clear understanding of:• What matrices are;• Performing basic operations on matrices;• Special forms of matrices;