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![Vectors And Matrices
• In MATLAB matrices are easy to define:
• Use ‘ ’ to separate row elements.
• Use ‘;’ to separate rows.
>> y = [1 2 3; 4 5 6; 7 8 9]
y =
1 2 3
4 5 6
7 8 9](https://image.slidesharecdn.com/intro1-181208165618/75/Introduction-to-MATLAB-1-11-2048.jpg)
![Vectors And Matrices
• Order of Matrix
◦m = no. of rows.
◦n = no. of columns.
• Vectors are special case
m = 1 row vector n = 1 column vector
A =
0.9501 0.6068 0.4231
0.2311 0.4860 0.2774m
n
>> x = [1 2 3 4]
x =
1 2 3 4
>> x = [1; 2; 3; 4]
x =
1
2
3
4](https://image.slidesharecdn.com/intro1-181208165618/75/Introduction-to-MATLAB-1-12-2048.jpg)
![Long Vector, Matrix
>> x = 1:10
x =
1 2 3 4 5 6 7 8 9 10
>> x = 1:0.5:5
x =
1 1.5 2 2.5 3 3.5 4 4.5 5
>> [1:4; 5:8]
x =
1 2 3 4
5 6 7 8
• If you want to create a row
vector, containing numbers
from 1 to 10, you write
• If you want to specify an
increment value other than
one, for example
• Also you can create a matrix
using the colon.](https://image.slidesharecdn.com/intro1-181208165618/75/Introduction-to-MATLAB-1-13-2048.jpg)
![Concatenation of Matrices
>> x = [1 2]
x =
1 2
>> y = [3 4]
y =
3 4
>> A = [x y]
A =
1 2 3 4
>> B = [x; y]
B =
1 2
3 4
• Given:
• you can create a matrix or construct one from other matrices.](https://image.slidesharecdn.com/intro1-181208165618/75/Introduction-to-MATLAB-1-22-2048.jpg)
![2D Plotting In MATLAB
• Note:
• The semicolon(;) tells MATLAB not to
display any output from that command.
>> x = [0:0.1:2*pi];
>> y = sin(x);
>> plot(x, y)
Sine function in range 0 ≤ x ≤ 2π.
• We are going to plot the function sin(x) between 0 ≤ x ≤ 2π.
• First, we define the range of the independent variable, x to be between 0 and
2π. i.e. between 0 and 360.
• Then, we define the dependent variable,
y by writing the command y = sin(x).
• We plot using the function, plot(x,y).](https://image.slidesharecdn.com/intro1-181208165618/75/Introduction-to-MATLAB-1-27-2048.jpg)
More Related Content
Similar to Introduction to MATLAB 1
Introduction to MATLAB 1
- 1.
- 2.
- 3. Outline • What Is MATLAB? • MATLAB Environment. •Variables. • Operators. • Vectors And Matrices. • Mathematical Functions. • Two Dimensional Plotting.
- 4. What is MATLAB? • MATLAB is a high-performance language for technical computing. •Stands for MATrix LABoratory. • MATLAB has many functions and toolboxes to help in various applications.
- 5.
- 6. MATLAB Environment Command Window • Type commands Current Folder • View folders and m-files Workspace •View program variables Command History • View past commands
- 7. Variables • There is no need to declare variable type in MATLAB. • All variables are created with double precision unless specified and they are matrices. •After these statements, the variables are 1x1 matrices with double precision. int a; double b; float c; Example: >> x=5; >> y=2;
- 8. Simple MATLAB Program >> x=5 x = 5 >>y=2 y = 2 >> ans = x * y ans = 10 • Note: • Creates the ans variable automatically when you specify no output argument.
- 9. Operators (arithmetic) Symbol Operation + Addition -Subtraction * Multiplication / Division ^ Power
- 10. Operators (arithmetic) >> 5 +7 ans = 12 >> 64 / 8 ans = 8 >> 12 * 5 ans = 16 >> 40 - 7 ans = 33 >> 2 ^ 5 ans = 32 >> 3 /0 ans = Inf >> 0/0 ans = NaN • Examples • Special Cases • Inf: Infinity. •NaN: Not a Number.
- 11. Vectors And Matrices • In MATLAB matrices are easy to define: • Use ‘ ’ to separate row elements. •Use ‘;’ to separate rows. >> y = [1 2 3; 4 5 6; 7 8 9] y = 1 2 3 4 5 6 7 8 9
- 12. Vectors And Matrices • Order of Matrix ◦m = no. of rows. ◦n = no. of columns. • Vectors are special case m = 1 row vector n = 1 column vector A = 0.9501 0.6068 0.4231 0.2311 0.4860 0.2774m n >> x = [1 2 3 4] x = 1 2 3 4 >> x = [1; 2; 3; 4] x = 1 2 3 4
- 13. Long Vector, Matrix >> x =1:10 x = 1 2 3 4 5 6 7 8 9 10 >> x = 1:0.5:5 x = 1 1.5 2 2.5 3 3.5 4 4.5 5 >> [1:4; 5:8] x = 1 2 3 4 5 6 7 8 • If you want to create a row vector, containing numbers from 1 to 10, you write • If you want to specify an increment value other than one, for example • Also you can create a matrix using the colon.
- 14. Creating Vectors, Matrices from functions >> x =zeros(2,3) x = 0 0 0 0 0 0 >> x = ones(1,3) x = 1 1 1 >> x = rand(1,3) x = 0.8147 0.9058 0.1270 • zeros(m,n) m x n matrix of zeros. • ones(m,n) m x n matrix of ones. • rand(m,n) m x n matrix of uniformly distributed random number in the interval (0,1).
- 15. Creating Vectors, Matrices from functions Function Description zeros(m,n) Matrix with all zeros ones(m,n)Matrix with all ones. eye(m,n) The identity matrix rand(m,n) Uniformly distributed random randn(m,n) Normally distributed random
- 16. Matrix Index • The matrix indices begin from 1 (not 0 (as in Java)). • The matrix indices must be positive integer. •Given: A = 1 2 3 4 5 6 7 8 9 >> A(4) ans = 2 >> A(1,2) ans = 2 >> A(3,:) ans = 7 8 9 >> A(:,2) ans = 2 5 8 >> A(1:2,1) ans = 1 4
- 17. Matrix Index • Given A = 12 3 4 5 6 7 8 9 >> A(-2), A(0) Error: Subscript indices must either be real positive integers or logicals. >> A(4,2) Error: Index exceeds matrix dimensions.
- 18. Matrices Operations • Given A and B: A= 1 2 3 4 5 6 7 8 9 B = 6 4 9 2 8 1 5 1 3 >> A + B ans = 7 6 12 6 13 7 12 9 12 >> A - B ans = -5 -2 -6 2 -3 5 2 7 6 >> A * B ans = 25 23 20 64 62 59 103 101 98 >> A’ ans = 1 4 7 2 5 8 3 6 9 • Subtraction• Addition • Product • Transpose
- 19. Matrices Operations (Element by Element) Symbol Operation .*Element-by-element multiplication ./ Element-by-element division .^ Element-by-element power
- 20. Matrix Functions Function Definition det Determinant diagDiagonal matrices and diagonals of a matrix eig Eigenvalues and eigenvectors inv Matrix inverse norm Matrix and vector norms rank Number of linearly independent rows or columns
- 21. Matrix Functions • Given: A= 1 2 3 4 >> det(A) ans = -2 >> diag(A) ans = 1 4 >> inv(A) ans = -2 1 1.5 -0.5 >> norm(A) ans = 5.4650
- 22. Concatenation of Matrices >> x =[1 2] x = 1 2 >> y = [3 4] y = 3 4 >> A = [x y] A = 1 2 3 4 >> B = [x; y] B = 1 2 3 4 • Given: • you can create a matrix or construct one from other matrices.
- 23. Mathematical Functions Function Definition FunctionDefinition sqrt(x) Square root exp(x) Exponential angle(x) Phase angle round(x) Round to nearest integer abs(x) Absolutevalue ceil(x) Round towards plus infinity rem(x) Reminder after division floor(x) Round towards minus infinity size(x) The dimensions of a matrix log(x) Natural logarithm min(x) Minimum value length(x) The length of a matrix max(x) Maximum value sign(x) Signum function
- 24. Trigonometric Functions Function Definition FunctionDefinition sin(x) Sine in radians sind(x) Sine in degrees cos(x) Cosine in radians cosd(x) Cosine in degrees tan(x) Tangent in radians tand(x) Tangent in degrees sec(x) Secant in radians secd(x) Secant in degrees csc(x) Cosecant in radians cscd(x) Cosecant in degrees cot(x) Cotangent in radians cotd(x) Cotangent in degrees deg2rad(x) Convert angle from degrees to radians rad2deg(x) Convert angle from radians to degrees
- 25. Trigonometric Functions (Inverse) Function Definition FunctionDefinition asin(x) Inverse sine in radians asind(x) Inverse sine in degrees acos(x) Inverse cosinein radians acosd(x) Inverse cosinein degrees atan(x) Inverse tangent in radians atand(x) Inverse tangent in degrees asec(x) Inverse secantin radians asecd(x) Inverse secantin degrees acsc(x) Inverse cosecant in radians acscd(x) Inverse cosecant in degrees acot(x) Inverse cotangent in radians acotd(x) Inverse cotangent in degrees
- 26. Trigonometric Functions >> sin(60) ans = -0.3048 >>cosd(60) ans = 0.5 >> asind(0.5) ans = 30 >> deg2rad(180) ans = 3.1416
- 27. 2D Plotting In MATLAB • Note: • The semicolon(;) tells MATLAB not to display any output from that command. >>x = [0:0.1:2*pi]; >> y = sin(x); >> plot(x, y) Sine function in range 0 ≤ x ≤ 2π. • We are going to plot the function sin(x) between 0 ≤ x ≤ 2π. • First, we define the range of the independent variable, x to be between 0 and 2π. i.e. between 0 and 360. • Then, we define the dependent variable, y by writing the command y = sin(x). • We plot using the function, plot(x,y).
- 28. Labels • title() • xlabel() •ylabel() >> title(‘Sine function in range 0 ≤ x ≤ 2π’) >> xlabel(‘Angles x’) >> ylabel(‘y = sin(x)’)