1. Matrices and Linear Transformations
Chapter 2
Matrices and Linear Transformations

2. Addition, Scalar Multiplication, and Multiplication of Matrices
Figure 2.1 An arbitrary m X n matrix A.

3. Figure 2.2 The elements of a square matrix A where the subscripts are equal, form the main diagonal.

4. Figure 2.3

5. Properties of Matrix Operations
Example 5
Figure 2.4

6. Figure 2.5

7. Example 6
Figure 2.6 Many networks are designed to accept signals at certain points and to deliver a modified version of the signals. Here, the usual arrangement is illustrated.

8. Example 6 (cont’d)
Figure 2.7 An example of a two-port.

9. Figure 2.8 Three two-ports with transmission matrices A, B, and C.

10. Exercise Set 2.2
Figure 2.9 Determine the transmission matrices of the two-ports.

11. Figure 2.10 A two-port that consists of three two-ports placed in series.

12. Matrix Transformations, Rotations, and Dilations
Figure 2.11

13. Figure 2.12

14. Figure 2.13 Rotation about the origin.

15. Figure 2.14 Matrix transformations.

16. Example 1
Figure 2.15

17. Figure 2.16

18. Figure 2.17

19. Theorem 2.9
Figure 2.18

20. Figure 2.19

21. Figure 2.20

22. Linear Transformations, Graphics, and Fractals
Figure Here, the structure preserving ideas of a linear transformation are illustrated.

23. Figure 2.22

24. Example 5
Figure 2.23

25. Figure 2.24 Fractal pictures of nature.

26. A Communication Model and Group Relationships in Sociology
Figure 2.25

27. Figure 2.26

28. Exercise Set 2.9
Figure 2.27

29. Figure 2.28

30. Figure 2.29

31. Figure 2.30