![Defining matrices in MATLAB
� 1D row vector – [1 2 3 4] or [1,2,3,4]
� 1D column vector – [1;2;3;4]
� 2D matrix – [1 2 3; 4 5 6; 7 8 9]
� Make a 1D row vector from 1 to 100. Tired ?
Use this – [1:1:100] or [1:100].
Try changing the step size.
� ‘:’ means ‘to’](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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- 1. MATRICES IN MATLAB Ritesh Kumar
- 2. Defining matrices in MATLAB � 1D row vector – [1 2 3 4] or [1,2,3,4] � 1D column vector – [1;2;3;4] � 2D matrix – [1 2 3; 4 5 6; 7 8 9] � Make a 1D row vector from 1 to 100. Tired ? Use this – [1:1:100] or [1:100]. Try changing the step size. � ‘:’ means ‘to’
- 3. Using Colon (:) � [1:4] gives a row vector containing [1 2 3 4] � [1:0.5:4] gives a row vector from 1 to 4 with a step size of 0.5 � Make a vector from 0 to 2π with a step size of 0.01
- 4. Matrix operators � Normal operations � A + B � A – B � A*B � A^2 � Dot (.) operations: Element wise operations � Y = A.^2 � Y = A.*B � Y = A.^B
- 5. Predefined functions for Matrices � Mathematical �sin, cos, tan �log, exp �sqrt � Creation �ones �zeros �eye �rand � Information �size �length
- 6. Predefined functions for Matrices � Matrix operations � sum � diag � transpose or ‘ � inv � det � eig � fliplr � reshape � flipud � rot90 � repmat
- 7. Matrix concatenation Suppose A, B, C are matrices � If we write [A B] or [A,B] � If we write [A;B] � Similarly [A B C] and [A;B;C] � [[A B];C]
- 8. Exercise � Create a vector of 20 elements in GP with first term 1 and common ratio ½. Calculate its sum � Calculate the sum of first 15 elements of the series
- 9. Indexing � Extracting elements from the arrays � Normal Indexing � Linear Indexing � Logical Indexing
- 10. Array indices � A is an n×m matrix � To extract the 5th row 6th column element we’ll write A(5,6) � The difference between Y=A(5,6) and A(5,6)=Y � Y=A(5,6) will extract the 5,6 element from A and save it to Y � A(5,6)=Y will change the 5,6 element to Y
- 11. Array indices � What if we wish to extract multiple columns or rows? � A([1 3 7],[1 2]) � Gives a sub-matrix containing elements which were in 1,3 and 7th row and 1 and 2 columns of matrix A � A([3 2 7],[3 2 3]) � A(:,[5 6]) � Here : means all � Gives a sub-matrix containing all rows and 5 and 6 columns of matrix A
- 12. Linear Indexing � A is 2D but we can use a single index to extract any element from A � A(5) � Same as A(2,2) A= 2 3 2 3 1 2 6 9 10
- 13. Exercise � Extract a diagonal of a square 5x5 matrix using linear indexing without using inbuilt command.
- 14. Logical indexing � Index with a matrix of 0 & 1 � Return those elements which corresponds to 1 � B=A>0; � C=A(B);
- 15. Exercise � Create a random matrix of 1x100. Change the elements to 0 which are smaller than 0.33 and 1 which are greater than 0.33 and smaller than 0.67 and 2 which are greater than 0.67
- 16. Exercise � A=[1 2 0 6 4 0 2]; � Get a B vector such that B=[1 ½ 0 1/6 ¼ 0 ½], i.e. reverse the elements which are not 0