The document discusses MATLAB vectors and matrices. It describes that MATLAB has row and column vectors. Row vectors are lists of numbers separated by commas or spaces within square brackets. Column vectors are similar but have elements separated by semicolons. Matrices are rectangular arrays of numbers with rows and columns. The document provides examples of defining, manipulating, and performing operations on vectors and matrices in MATLAB.

1. EngMahmoud Hussein

2. Vectors
MATLAB has two forms of vectors:
 Row vectors
 Column vector
 Row vectors: they are lists of numbers separated by either commas or
spaces.
 The number of entries is known as the"length" of the vector The
entries must be enclosed in square brackets.
v=[1 3,sqrt(25)];

3. Vectors
 Examples:
 v = [ 1 3, sqrt(5)]
 v2 = [3+ 4 5]
 v3 = [3 +4 5] � is v2=v3 ?!!!!!
 We can do certain arithmetic operations with vectors of the same length
(v , v3)
 Try adding v and v2.

4. Vectors
Suppose we want a vector starting from 1 up to 100 with increments of
one (i.e. 1 2…100).
Write 100 elements � time consuming process.
 An easy way: v=[1:100].
 Generally a : b : c produces a vector of entries
 Starting with the value a,
 Incrementing by the value b
 Until it gets to c.
 Example: 0.32:0.1:0.6

5. Vectors
 So far, we have two methods for declaration:
 X=[element1 element2 element3 ……. ]
 (start : step : end)
 Another declaration of the vector is:
 Z=linspace(O,1O,11) � (start, end, no. of points)
 Linear space
 Increment = (end - start)/(N-1)
 If X is a vector, then Y=sin(X), is also a vector with the same dimensions.
this direct relation between x,y

6. Coloum Vectors
 These have similar constructs to row vectors.
 But, entries are separated by ";" instead of ",".
 Or, write each element in separate row.
 >>x=[2;3;4];
 X=2
3
4
 >>x=[2
3
4]

7. Vectors Transposing
 We can convert a row vector into a column vector (and vice versa) by a
process called transposing.
 If H is a row vector, then
 H' is a column vector, with elements of H.
 Try it.
 >>x=[2;3;4]; x’
 >>x=[2 3 4]; x’
 If x is a complex vector, then x' gives the complex conjugate transpose
of x.

8. Operations on Vectors

9. Operations on Vectors

10. vectors notes
 Assume r = [1:2:6, -1:-2:-7];
 >>r^2
 >>r.^2
 to get the square of each element we use: X.A2 NOT XA2
 Where (.) means element by element and no care for dimension.

11. vectors multipulication
 What is the difference?
Z = X*Y � single valued
Z = X.*Y � vector!
Assume x=[1 2 3 4]
y=[5 6 7 8]

12. plotting two vectors
 Note: minimizing the step size will lead to very smooth curve for the
relationship and vice versa.
 Simply we use the plot order to plot the vectors against each other.
 Plot (indep_var , depen_var)
 >>x=[-2*pi:0.1:2*pi];
 >>y=sin(x);
 >>plot(x,y)

13. plotting two vectors

14. plotting two vectors
 Note: no direct relation bt. Month and Temp
 Solution:
 >> Month=[1:1:12];
 >> Temperature=[ 17 19 22 24 27 30 34 35 31 26 23 20];
 >> plot(Month,Temperature)
 The result is a continuous curve, but do we need that really in this
application?
 Use stem(Month,Temperature) for discrete sample plotting.

15. Plotting two vectors

16.  Strings is declared as follows:
 t1 = 'A' � 1-by-1 character array.
 t2 = 'BCDE' � 1-by-4 character array Powerful operations can be
performed using just one or two commands.
 If our string contains quotes (you're the one)
 >> str = 'you''re the one' � use 2 quotes
 You can convert between ASCII values and the characters they
represent using the double and char command.
Strings on matlab

17.  >>Alpha=‘mahmoud’;
 >>num=double(alpha);
 >>char(num)
ans= mahmoud
Strings on matlab

18. matrices
 Row and Column vectors are special cases of matrices.
 An m x n matrix is a rectangular array of numbers having m rows and
n columns.
 A=[1 2 3
4 5 6]

19. Typing matrices
 To type a matrix into MATLAB you must:
 Begin with a square bracket [
 Separate elements in a row with commas or space
 Use a semicolon ";" to separate rows
 End the matrix with another square bracket ].
 Example: a=[123;456]
 MATLAB responds with:
a=1 2 3
4 5 6

20. Concatenating Matrices
 Matrices can be made up of sub-matrices:
 Try this:

21. Matrix replication
 The repmat function can be used to replicate a matrix.
 repmat( matrix, No. replecated rows, No. rep columns);
 Try this:

22. Matrix generator

23. Operation on matrices

24. Operation on matrices

25. Operation on matrices

26. Operation on matrices

27. Extracting bits of matrix
 Given Matrix J, what is the result of the following?
j=1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
J(1,1), J(2,3), J(4,3), J(:,3), J(4,:), J(1:3,2:3),

28. Deleting row or coloum
 Let a is a predefined matrix
 To delete row number M, write:
a(M,:) = []
 To delete column number N, write:
a(:,N) = []

29. Solving linear equation
 Suppose that you would like to solve the following system of equations:
 2X+Y-Z=6
 X-Y-Z=-3
 X+2Y-3Z=-9
 In matrix form, you can write:

30. Solving linear equation