1. Chapter 2 Creating Arrays Legend: MATLAB command or syntax : Blue MATLAB command OUTPUT : LIGHT BLUE

2. Vector – a 1D row or column Several ways of creating a vector: 1. Specifying EACH element Row Vector Elements separated by space or comma. e.g. p = [1 2 3 4 5] OR p = [1, 2, 3, 4, 5] p = 1.00 2.00 3.00 4.00 5.00 Column Vector Elements separated by semi- colon (;). e.g. q = [1; 2; 3; 4; 5] q = 1.00 2.00 3.00 4.00 5.00

3. Several ways of creating a vector: 2. Specify 1 st term, last term, and spacing(constant) between each element variable_name = [m : q : n] OR variable_name = m : q : n *spacing could be positive or negative.*If spacing is omitted, the default is 1. e.g. a = [1 : 2 : 11] a = 1 3 5 7 9 11 b = [12 : -3 : 0] b = 12 9 6 3 0 c = [1 : 5] ?? c = 1 2 3 4 5 1 st term spacing last term

4. Several ways of creating a vector: 2. Specify 1 st term, last term, and number of terms variable_name = linspace(f, l, n) where f: first term; l : last term ; n : # of terms * If n is omitted, default is 100. e.g. v = linspace(0, 10, 5) v = 0 2.50 5.00 7.50 10.00 e.g. w = linspace(1, 50, 1000);

5. Transpose of a Vector Row and column vectors are transpose of each other. To convert a row vector a to a column vector b, type the transpose operator, a single quote (‘) after the vector name. e.g. >> a = linspace(2,10,5) a = 2 4 6 8 10 >> b = a' b = 2 4 6 8 10

6. Addressing elements of a vector Addressing a range of elements. For example, addressing elements between and including positions 2 and 5 >> a = v(2:5) a = 8 6 4 2 Re-assign value of 0 to 5th element. >> v(5) = 0 v = 10 8 6 4 0 0 >> v(1) * v(5) + v(2) ans = 8

7. Manipulating Vectors (Adding and Deleting Elements) Add elements to vector by assigning new elements. e.g. >> v = [1 2 3 4 ] v = 1 2 3 4 >> v(6) = 6 v = 1 2 3 4 0 6 Delete elements from vectors : by assigning element(s) to [] e.g. >> v(5) = [] v = 1 2 3 4 6 >> v(2:3) = [] v = 1 4 6

8. Facts about Matrices A 2D array of rows and columns. An mXn matrix has m rows and n columns. Square Matrix : # of rows = # of columns = n(say) Then square matrix would be nXn Identity Matrix : Diagonal elements are ones; non-diagonal elements are zeros Zero matrix : All elements are zeros.

9. Facts about Matrices Examples of matrices A 3X4 matrix (3 rows and 4 columns) 1 2 3 4 5 6 7 8 9 10 11 12 A 3X3 identity matrix 1 0 0 0 1 0 0 0 1 A 2X3 zero matrix 0 0 0

10. Matrices in MATLAB Creating a matrix Variable_name = [r1e1 r1e2..…r1en; r2e1 r2e2… r2en;……. rne1 rne2 …rnen] where r1e1 : row 1 element 1 and so on e.g. a = [1 2 3 ; 4 5 6 ; 7 8 9] a = 1 2 3 4 5 6 7 8 9 *elements of a matrix(or vector) can be numbers, math expressions, predefined variables and/or functions.

11. Matrices in MATLAB Zero matrix : zeros(m,n) Ones matrix : ones(m,n) m : # of rows; n : # of columns Identity matrix : eye(n) N : # of rows and columns e.g. >> zeros(2,3) ans = 0 0 0 >> eye(3) ans = 1 0 0 0 1 0 0 0 1 Transpose of a matrix : rows and columns are interchanged. e.g. >> a = [1 2 3;4 5 6;7 8 9] a = 1 2 3 4 5 6 7 8 9 >> b = a' b = 1 4 7 2 5 8 3 6 9

12. Addressing Matrices By specifying the row and column of the element, we specify its position. Position of 1 st element of a matrix A is A(1,1). A(:,n) Refers to elements in ALL ROWS of column n of matrix A. A(m,:) Elements in ALL COLUMNS and row n. A(:,m:n) Elements in ALL ROWS of columns m through n A(m:n,:) Elements in ALL COLUMNS and rows m through n. A(m:n,p:q) Elements in rows m through n and columns p through q. Addressing Matrices

13. Manipulating Matrices (Adding and Deleting Elements) Adding elements to matrix: >> V= [1 2 3; 4 5 6] V = 1 2 3 4 5 6 >> V(5,:) = ones(1,3) V = 1 2 3 4 5 6 0 0 0 1 1 1 Deleting elements from matrix >> V(3:4, :) = [] V = 1 2 3 4 5 6 1 1 1 V(2,2) =[] ?? ??? Subscripted assignment dimension mismatch.

14. Vectors length(v) : returns number of elements in vector v diag(v) : creates a square matrix (from the vector v), with elements of v in the diagonal. e.g. >> v = [1 2 3 ]; >> d = diag(v) d = 1 0 0 0 2 0 0 0 3 >> l = length(v) l = 3 Other Built-In Functions Matrices Size(A) : returns row vector [m,n], where m and n are size m X n of the matrix. diag (A) : Creates a vector from the diagonal elements of matrix A. reshape (A,m,n) : creates an m X n matrix from A. elements are taken column after column. A must have m times n elements. e.g. >> A = [1 2 3 ; 4 5 6]; >> s = size(A) s = 2 3 d = (diag(A))' d = 1 5 >> B = reshape(A, 2,3) B = 1 2 3 4 5 6

15. Strings String is an array of characters. It can include letters, digits, other symbols, and spaces. It’s created by typing characters within single quotes. e.g. ‘MATLAB’, ‘34&g’, ‘h!#ji464’. e. g.>> S = 'It is MATLAB time!!' S = It is MATLAB time!! >> size(S) ans = 1 19 Are n = 123 and s = ‘123’ same?? NO >> size(n) ans = 1 1 >> size(s) ans = 1 3 To create a matrix of strings, each row should have the same number of elements. This can be done using a built-in function called char. Char creates an array with each row having same number of elements. It makes the length of each row same as the longest row by adding spaces. e.g. >> Emp = char('Employee Name', 'Employee Number', 'Department') Emp = Employee Name Employee Number Department