Basics of Matlab for students and faculty

Mar 18, 20240 likes44 views

1) Matrices can be defined as row vectors, column vectors, or 2D matrices in MATLAB. Common operations include addition, subtraction, multiplication, and exponentiation. 2) Predefined functions like ones, zeros, eye, and rand can be used to create matrices. Other functions like sum, diag, transpose, inv, and det perform operations on matrices. 3) Matrices can be concatenated horizontally using [A B] or vertically using [A;B]. Elements can be indexed and extracted from matrices using normal, linear, or logical indexing.

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’

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

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

Predefined functions for Matrices
� Mathematical
�sin, cos, tan
�log, exp
�sqrt
� Creation
�ones
�zeros
�eye
�rand
� Information
�size
�length

Predefined functions for Matrices
� Matrix operations
� sum
� diag
� transpose or ‘
� inv
� det
� eig
� fliplr
� reshape
� flipud
� rot90
� repmat

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]

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

Indexing
� Extracting elements from the arrays
� Normal Indexing
� Linear Indexing
� Logical Indexing

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

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

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

Exercise
� Extract a diagonal of a square 5x5 matrix
using linear indexing without using inbuilt
command.

Logical indexing
� Index with a matrix of 0 & 1
� Return those elements which corresponds to 1
� B=A>0;
� C=A(B);

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

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

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Basics of Matlab for students and faculty

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

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