1. CMPS 1371 Introduction to Computing for Engineers VECTORS

2. ARRAYS The real strength of Matlab is in matrix manipulations Arrays are homogeneous collection of things. All are the same Are indexable

3. VECTORS Our simplest array type is called a vector. Simple example: ODDS = [ 1 3 5 7 9 11 13 15] To index a vector, need to know the position within the vector: First element has position 1 (NOT ZERO!) ODDS(1) = 1 Last element: either the length of the array or the special label ‘end’ ODDS(8) = 15 ODDS(end) = 15

4. Create a Vector To create a row vector, enclose a list of values in brackets

5. Create a Vector You may use either a space or a comma as a “delimiter” in a row vector

6. Create a Vector Use a semicolon as a delimiter to create a new row

7. Shortcuts While a complicated matrix might have to be entered by hand, evenly spaced matrices can be entered much more readily. The command b= 1:5 or the command b = [1:5] both return a row matrix

8. The default increment is 1, but if you want to use a different increment put it between the first and final values Increments

9. To calculate spacing Use linspace Initial value in the array Final value in the array number of elements in the array

10. Basic Functions Some basic functions: Consider temp = [1 2 3 4 5] length(temp)=5 sum(temp)=15 mean(temp)=3 median(temp)=3

11. Calculations Matrices can be used in many calculations with scalars There is no confusion when we perform addition and subtraction Multiplication and division are a little different In matrix mathematics the multiplication operator (*) has a very specific meaning regarding Matrix multiplication We will use (.*) for matrix multiplication We can use (*) for scalar multiplication

12. Adding Vectors

13. Addition between arrays is performed on corresponding elements

14. Multiplying Vectors MATLAB interprets * to mean matrix multiplication. The arrays a and b are not the correct size for matrix multiplication in this example Multiplication between arrays is performed on corresponding elements if the.* operator is used

15. Array Operations Array multiplication.* Array division./ Array exponentiation.^ In each case the size of the arrays must match

16. Changing the Vector Easy to add elements to the array Temp = [1 2 3 4]; Temp(5) = 8;  Temp now has 5 elements 1, 2, 3, 4, 8 Can also concatenate fred = [[1,2,3,4] [3,4,5,]] fred = [fred 4 5 6 7] Can also remove elements by using the "Null" vector A = [ 1 2 3 4 5 6 7 ] A(2) = [ ] – now what is A