1. Creating scalars, vectors, matrices Ex1 & 2. Dot Product & Cross Product Ex3. Plotting Graphs Ex4. Conversion Table Ex5. Plotting functions Finishing Ex4. Ex6 and Ex7. Use of matrices in real world Creating Arrays 11

2. 1. Creating scalars Assign a value to a variable (i.e. Hardcode) pressure = 10; %pascals temperature = 298; %kelvin Store the result of an equation pressure = density*R*temperature; Save the return-value of the input() command age = input(‘Enter your age: ’); 22

3. 2. Creating vectors There are LOTS of ways to create vectors, based on three simple ideas: The values in the vector are pre-defined. For example: [ 2 -5 4.4 -96.6] 33

4. 2. Creating vectors There are LOTS of ways to create vectors, based on three simple ideas: The values in the vector are pre-defined. For example: [ 2 -5 4.4 -96.6] The values have a pattern (addition only). For example: [10, 20, 30,…100] or [-10 -8 -6 -4 -2 0] 44

5. 2. Creating vectors There are LOTS of ways to create vectors, based on three simple ideas: The values in the vector are pre-defined. For example: [ 2 -5 4.4 -96.6] The values have a pattern (addition only). For example: [10, 20, 30,…100] or [-10 -8 -6 -4 -2 0] Finally, the total amount of values is known. For example: 25 points evenly spaced from 0 to 100. 55

6. 2.1. Pre-defined values 66

7. 77 2.1. Pre-defined values, cont.

8. 88

9. 99 What else are semi-colons used for? 2.1. Pre-defined values, cont.

10. 10 What else are semi-colons used for? They create rows AND suppress output! 2.1. Pre-defined values, cont.

11. 11 What else are semi-colons used for? They create rows AND suppress output! The apostrophe allows to transpose a vector. Rows become columns. Columns become rows. 2.1. Pre-defined values, cont.

12. 12 What else are semi-colons used for? They create rows AND suppress output! The apostrophe allows to transpose a vector. Rows become columns. Columns become rows. What dimension will speeds have? _______________________________ 2.1. Pre-defined values, cont.

13. Ex1. Dot product Remember the DOT product? (maybe/maybe not) 13 Credits to: http://www.itee.uq.edu.au/~c ogs2010/cmc/chapters/Hebbi an/ten5.gif http://www.itee.uq.edu.au/~c ogs2010/cmc/chapters/Hebbi an/ten5.gif The DOT product…

14. Ex1. Dot product Remember the DOT product? (maybe/maybe not) 14 Credits to: http://www.itee.uq.edu.au/~c ogs2010/cmc/chapters/Hebbi an/ten5.gif http://www.itee.uq.edu.au/~c ogs2010/cmc/chapters/Hebbi an/ten5.gif In Matlab The DOT product…

15. *** * * * Ex2. Cross product How about the CROSS product? (maybe/maybe not) 15 Source: http://www.math.umn.edu/~nykamp/m 2374/readings/crossprodex/ http://www.math.umn.edu/~nykamp/m 2374/readings/crossprodex/ Source: Wikipedia The CROSS product…

16. Cross product, cont. 16 In Matlab

17. Ex3. Plotting graphs In order to plot, Matlab needs data points: 17 x y -7 -2 3 8 4 -7 3 x y

18. Ex3. Plotting graphs In order to plot, Matlab needs data points: 18 x y -7 -2 3 8 4 -7 3 x y

19. Ex3. Plotting graphs In order to plot, Matlab needs data points: 19 x y -7 -2 3 8 4 -7 3 x y Matlab connects the dots!

20. Ex3. Plotting graphs In order to plot, Matlab needs data points: Well… x is an array of data points x = [-7 -2 3 8] y is another array of data points y = [4 -7 3 -1] …for the curious ones, to plot: plot(x,y) 20 x y -7 -2 3 8 4 -7 3 x y

21. 2.2. Patterns (addition only) 21 The range operator Numbers are separated by +1

22. 22 The range operator Numbers are separated by +1 An additional value in the middle specifies the increment. +3 +3 +3 +3 +3 +3 +3 +3 >32  2.2. Patterns, cont.

23. 23 The range operator Numbers are separated by +1 An additional value in the middle specifies the increment. +3 +3 +3 +3 +3 +3 +3 +3 >32  -2.5 -2.5 -2.5 < 3  Go reverse by using a negative increment! CAUTION: the beginning number must be > the end number. Here 10>3. (This also shows it works with decimals.) 2.2. Patterns, cont.

24. 24 The range operator Numbers are separated by +1 An additional value in the middle specifies the increment. +3 +3 +3 +3 +3 +3 +3 +3 >32  -2.5 -2.5 -2.5 < 3  To use the apostrophe and create a column vector, absolutely place brackets first! … else…. 2.2. Patterns, cont.

25. 25 The range operator Numbers are separated by +1 An additional value in the middle specifies the increment. +3 +3 +3 +3 +3 +3 +3 +3 >32  -2.5 -2.5 -2.5 < 3  To use the apostrophe and create a column vector, absolutely place brackets first! … else…. Only the scalar -10 gets transposed: but a scalar transposed remains the same scalar! 2.2. Patterns, cont.

26. Ex4. Conversion table % create celsius data points celsius = 0:10:100; %0 to 100 by +10 increment % calculate Fahrenheit fahrenheit = celsius * 9/5 + 32; % show table 26

27. 2.3. Specific amount of data points A built-in function called linspace() spaces elements linearly in an array. What does this mean? The distance between each consecutive data point is equal. There are two ways to use it, as Matlab ‘hints’ when the command typed is unfinished: 27 Either provide 2 arguments, or provide 3 arguments.

28. 2.3. linspace(), cont. 28 The third argument indicates the ________________________.

29. 29 The third argument indicates the ________________________. When Matlab cannot display all the elements on one line, it simply indicates the column-number per line. 2.3. linspace(), cont.

30. 30 The third argument indicates the ________________________. When Matlab cannot display all the elements on one line, it simply indicates the column-number per line. 2.3. linspace(), cont.

31. 31 ?????? %no third argument Omit the third argument uses a default of _______ data points! 2.3. linspace(), cont.

32. Ex5. Plotting graphs Suppose a function that relates each x to its y-coordinate is known: y = f(x) = x 2.  Plot y vs. x. 32

33. Ex5. Plotting graphs Suppose a function that relates each x to its y-coordinate is known: y = f(x) = x 2.  Plot y vs. x. In this case, it is tedious work to hard-code each x and y array. Are 4 data-points sufficient, like in example 3? 33 x y x y -10 -5 5 10 100 25 100

34. Ex5. Plotting f(x) = x^2, cont. Remember: which built-in function influences the number of data-points in an array?____________________ In this case: %array x of 20 data points %calculate array of y’s. %plot command And the result is… 34

35. Ex5. Plotting f(x) = x^2, cont. Remember: which built-in function influences the number of data-points in an array?____________________ In this case: %array x of 20 data points x = linspace(-10,10,20); %calculate array of y’s. y = x.^2; %(The dot will be explained next time…) %plot command plot(x,y) And the result is… 35

36. Ex5. Plotting f(x) = x^2, cont. 36 Does this represent f(x) = x 2 ? Yes Or No Yes, but it took 20 points!!

37. Ex5. Plotting f(x) = x^2, cont. The use of linspace() in this example is crucial! Why do all 20 data point need to be linearly spaced? What would happen otherwise? 37 Still 20 points!!.. but the first 19 are before -5,.. and the last one is 10. Not f(x) = x 2..

38. 3. Creating Matrices Simply a combination of all symbols introduced with vectors! Square brackets [ ] Spaces or commas,, Semi-colons ; Apostrophes ’ 38

39. 3.1. Matrices: hard-coding 39 Use semi-colons to create new rows. ONLY rectangular matrices:  The number of columns MUST match for each row, and vice-versa.

40. 40 Use semi-colons to create new rows. ONLY rectangular matrices:  The number of columns MUST match for each row, and vice- versa. Use previous matrices to actually create new matrices. This example transposes the matrix variable a. 3.2. Reusing Previous matrices

41. 41 Use semi-colons to create new rows. ONLY rectangular matrices:  The number of columns MUST match for each row, and vice- versa. You can use previous matrices to actually create new matrices. This example transposes the variable a. Combine any previous methods, AS LONG AS the matrix remains rectangular. 3.3. Using Colons

42. 3.4. “Concatenating” 42 Use semi-colons to create new rows. ONLY rectangular matrices:  The number of columns MUST match for each row, and vice- versa. You can use previous matrices to actually create new matrices. This example transposes the variable a. You can combine any previous methods, AS LONG AS the matrix remains rectangular. Finally, create arrays by combining previous variables! This is called CONCATENATING.

43. 43 Use semi-colons to create new rows. ONLY rectangular matrices:  The number of columns MUST match for each row, and vice- versa. You can use previous matrices to actually create new matrices. This example transposes the variable a. You can combine any previous methods, AS LONG AS the matrix remains rectangular. When the array becomes too big, the numbers no longer display. 3.5. Using the command window

44. Ex4. Conversion table, end! % create celsius data points celsius = 0:10:100; %0 to 100 by +10 increment % calculate Fahrenheit fahrenheit = celsius * 9/5 + 32; % show table [celsius’ fahrenheit’] 44

45. Ex6. Sling Thermometer 45 A method to read relative-humidity.

46. Ex7. Images 46 Each row and column have a pixel value stored.

47. Wrapping Up Know by heart each way to create a row/column vector. Hard-code each data point Separate each data-point by comma or spaces for row vector Separate each data-point by semicolon for a column vector Shortcut when there is an addition pattern (colon) Shortcut when a specific amount of data points are linearly spaced ( linspace() ) 47

48. Wrapping Up Know by heart each way to create a row/column vector. Hard-code each data point Separate each data-point by comma or spaces for row vector Separate each data-point by semicolon for a column vector Shortcut when there is an addition pattern (colon) Shortcut when a specific amount of data points are linearly spaced ( linspace() ) Realize that creating matrices only requires combining all of the above, while respecting one crucial rule: A matrix must remain rectangular at all times (i.e. no holes within the matrix) 48

49. Wrapping Up Know by heart each way to create a row/column vector. Hard-code each data point Separate each data-point by comma or spaces for row vector Separate each data-point by semicolon for a column vector Shortcut when there is an addition pattern (colon) Shortcut when a specific amount of data points are linearly spaced ( linspace() ) Realize that creating matrices only requires combining all of the above, while respecting one crucial rule: A matrix must remain rectangular at all times (i.e. no holes within the matrix) What does the apostrophe do? 49

50. Wrapping Up Know by heart each way to create a row/column vector. Hard-code each data point Separate each data-point by comma or spaces for row vector Separate each data-point by semicolon for a column vector Shortcut when there is an addition pattern (colon) Shortcut when a specific amount of data points are linearly spaced ( linspace() ) Realize that creating matrices only requires combining all of the above, while respecting one crucial rule: A matrix must remain rectangular at all times (i.e. no holes within the matrix) What does the apostrophe do? Restate some examples of vector operations and matrix operations. 50