MATLAB – Array Creation

1. MATLAB – Array Creation Chapter 2 • Topics Covered: • Creating vectors • row vectors • column vectors • Creating matrices

2. What is a vector? • A Scalar is a single number. • example 15 • A Vector is an ordered list of several numbers. • Row vector– a horizontal list of numbers • example 1 2 5 8 • Column vector– a vertical list of numbers • example 3 • 5 • 7

3. Examples of Vectors A vector is an ordered list of numbers. The list of even numbers from 2 to 10: 2 4 6 8 10 The average temperatures for January, February, March, April and May: 28 33 42 56 67

4. Creating row vectorsin MATLAB A row vector is created by typing the elements (numbers) inside square brackets [ ] and separated by commas or spaces. >> vr = [ 2, 4, 5 ] >> vr = [ 2 4 5 ] vr = 2 4 5 vr = 2 4 5 Note: the name of a vector can be any valid MatLab variable name. In this case 'vr' stores three numbers – in vector format.

5. Creating column vectors in MATLAB A column vector is created by typing the elements (numbers) inside square brackets [ ] separated by a semicolon or an enter. >> vc = [ 2 ; 4 ; 5 ] vc = 2 4 5 >> vc = [ 2 4 5 ] vc = 2 4 5

6. Creating a vector with constant spacing A vector in which the first term is first, the spacing is space and the last term is last can be created by typing [ first : space : last ] Create the list of odd numbers from 1 to 13 >> v1 = [ 1 : 2 : 13 ] v1 = 1 3 5 7 9 11 13 If space is omitted, the default space is 1 >> v2 = [ 3 : 7 ] v2 = 3 4 5 6 7

7. Examples of constant spacing Create a vector called v3 with numbers divisible by 7 from -63 to -28 >> v3 = [ -63 : 7 : -28 ] v3 = -63 - 56 - 49 - 42 - 35 -28 Create a vector called v4 from 3.1 to 2.3 with a difference of 0.1 between the elements >> v4 = [ 3.1 : -0.1 : 2.3 ] v4 = 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3

8. Using the linspace(first, last, n) function Create a vector v5 with 6 elements, starting at 2.5 and ending at 3.5 >> v5 = linspace(2.5, 3.5, 6) v5 = 2.50 2.70 2.90 3.10 3.30 3.50 Create a vector v6 with 10 elements, starting at 99 and ending at 33 >> v6 = linspace(99, 33, 10) v6 = 99.0 91.7 84.3 77.0 69.7 …. 33.0

9. Vector Examples Cont’d Create a vector A with 4 elements. The first element is 3, the second is 32 , the third is 33 and fourth is 34 >> A = [ 3 3^2 3^3 3^4 ] A = 3 9 27 81 OR >> x =3; >> A = [ x x^2 x^3 x^4] A = 3 9 27 81

10. What is a Matrix ? • Scalars – numbers that represent a single value • Vectors - representation of a group of scalar numbers • Row vector – horizontal group of numbers • Column vector – vertical group of numbers • Matrix – Two dimensional representation of a group of scalar numbers containing rows and columns • example : 2 4 6 8 • 1 2 3 4

11. Matrix : Example Suppose we want to represent the attendance of 3 students (X, Y and Z) in 4 months (Jan, Feb, March and April) in a concise form. We can create a matrix as follows: 10 10 9 8 9 7 6 9 7 10 7 6 Jan Feb Mar Apr Student X Attendance = 3 Rows Student Y Student Z 4 Columns • A (m x n), or “m by n”, matrix has m rows and n columns. • (mx n) is called the size of the matrix. • In this example Attendance is a 3 x 4 matrix.

12. Creating a Matrix in MATLAB A Matrix is created by typing the elements (numbers) row by row inside square brackets [ ], separated by semicolons or enter. >> A = [5 35 43 4 76 81 21 32 40] A = 5 35 43 4 76 81 21 32 40 >> A = [5 35 43; 4 76 81; 21 32 40] A = 5 35 43 4 76 81 21 32 40