Chapter 2

Creating Arrays

Legend: MATLAB command or syntax : Blue

MATLAB command OUTPUT : LIGHT BLUE

Vector – a 1D row or columnSeveral 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

Several ways of creating a vector:2. Specify 1st term, last term, and

spacing(constant) between each elementvariable_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 11b = [12 : -3 : 0]b = 12 9 6 3 0c = [1 : 5] ??c = 1 2 3 4 5

1st term spacing

last term

Several ways of creating a vector:2. Specify 1st 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);

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

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

• Position of the 1st element in a vector is 1.• So, for a vector v, the element is addressed as v(k).• e.g. >> v = [10 : -2 : 0]v = 10 8 6 4 2 0

• Addressing specific elements

>> v(1) * v(5) + v(2) ans = 28• Addressing ALL elements of vector>> a = v(:)a =

10 8 6 4 2 0

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) = 6v = 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

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.

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 0 0 0

Matrices in MATLAB

• Creating a matrixVariable_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.

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 columnse.g. >> zeros(2,3)ans = 0 0 0 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

Addressing Matrices

• By specifying the row and column of the element, we specify its position.

• Position of 1st 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

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 0 0 0 1 1 1

Deleting elements from matrix>> V(3:4, :) = []V = 1 2 3 4 5 6 1 1 1V(2,2) =[] ????? Subscripted assignment dimension mismatch.

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 FunctionsMatrices

• 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

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 NumberDepartment