1. Dr. Ameria Eldosoky Discrete mathematics
Discrete Mathematical Structures: Theory and Applications

2. Matrices

3. Matrices

4. Matrices

5. Matrices

6. Matrices

7. Matrices

8. Matrices
Two matrices are added only if they have the same number of rows and the same number of columns
To determine the sum of two matrices, their corresponding elements are added

9. Matrices

10. Matrices

11. Matrices

12. Matrices

13. Matrices
The multiplication AB of matrices A and B is defined only if the number of rows and columns of A is the same as the number of rows and of B

14. Matrices
Figure 4.1
Let A = [aij]m×n be an m × n matrix and B = [bjk ]n×p be an n × p matrix. Then AB is defined
To determine the (i, k)th element of AB, take the ith row of A and the kth column of B, multiply the corresponding elements, and add the result
Multiply corresponding elements as in Figure 4.1

16. Matrices

18. Matrices
The rows of A are the columns of AT and the columns of A are the rows of AT

20. Matrices Boolean (Zero-One) Matrices Matrices whose entries are 0 or 1
Allows for representation of matrices in a convenient way in computer memory and for design and implement algorithms to determine the transitive closure of a relation

21. Matrices Boolean (Zero-One) Matrices
The set {0, 1} is a lattice under the usual “less than or equal to” relation, where for all a, b ∈ {0, 1}, a ∨ b = max{a, b} and a ∧ b = min{a, b}

22. Matrices

23. Matrices

24. Matrices