Introduction to MATLAB

• MATLAB is a mathematical and graphical software package
• Functions in MATLAB operate with vectors and matrices
• It is a package for numerical, graphical, and programming tasks
• MATLAB has built-in functions and supports toolboxes for added functionality
• It is used in engineering, science, finance, and economics for calculations, plotting, and algorithm implementation
• The central screen is the Command Window
• The Command Window displays ">>" or ">", known as the prompt
• MATLAB can be used interactively by entering commands at the prompt
• Programs can be written in script files or M-files
• The Workspace shows available variables, and the Current Folder shows folders and script files
• demo brings up MATLAB examples in the Help Browser
• help explains a function; help help explains how the help function works
• lookfor searches the help for a specific word or phrase
• doc opens a documentation page in the Help Browser
• To exit MATLAB, type quit or exit, or close the program
• Variables store values in a MATLAB session or program
• The Workspace Window displays created variables and their values
• Initializing a variable is assigning its first value
• An assignment statement is in the format variablename = expression
• MATLAB uses 'ans' as a default variable if an expression is typed without assignment
• The up arrow key recalls previously typed commands
• Scalars are plain numbers
• Vectors are lists of numbers
• Matrices are tables of numbers
• All variables are represented as matrices
• size(x) reports the dimensions of x
• Row vectors can be created by enclosing values in square brackets, separated by spaces or commas
• Typing y = [1 2 3]; suppresses the printout of the value of y
• The colon operator can be used to iterate through regularly spaced values in a vector
• 1:5 results in integers from 1 to 5
• A step value can be specified with the colon operator: first:step:last
• The linspace(x,y,n) function creates a linearly spaced vector with n values between x and y
• If n is omitted, the default is 100 points
• The logspace(x,y,n) function creates a logarithmically spaced vector from 10^x to 10^y
• If n is omitted, the default is 50 points
• Vector variables can be created by concatenating existing variables: newvec = [nv ls]
• Matrices are created by separating rows with semicolons: A = [1 2; 3 4]
• Vectors/matrices dimensions are important for working with them
• The colon operator iterates values in rows
• Separate rows can be specified by hitting Enter after each row
• Matrices of random numbers are created using the rand function.
• rand(n) creates an n x n matrix
• rand(rows, columns) specifies the number of rows and columns
• Matrices of random integers are generated using randi
• The range and dimensions of the matrix is set with randi([min, max], rows, columns)
• A row vector can be transposed into a column vector using the apostrophe operator: y = y'
• Column vectors can be initialized using semicolons: y = [1;2;3]
• Elements within a matrix are accessed using A(i,j) for the element in the ith row and jth column
• A colon can be used to access an entire row or column of a matrix
• A(1,:) produces all elements in the first row
• A(:,2) produces all elements in the second column
• A(:,:) calls all elements of Matrix A
• For a vector, only one position is required to call element
• Individual matrix elements can be modified by assigning a new value: mat(1,2) = 11
• An entire row or column can be changed by assigning a vector of the correct length
• The correct length must be assigned when modifying a row

Matrix Modifications

• Individual element cannot be added if it changes the shape
• An entire row or column can be added
• Gaps between the current matrix and added rows/columns are filled with zeros
• The syntax A(2:3, 2:3) accesses a range of elements

Value Ranges

• Calling syntax creates ranges
• Calling 1:10 produces numbers from 1 to 10
• Variable assignment can be performed using assignment operator

Multi-Dimensional Limitations

• MATLAB supports tensors
• Data structures called tensor are multi-dimensional matrices
• Tensors can act like cube or hypercube in their data structure

Numerical Expressions

• Created using values, variables, operators, built-in functions, and parentheses
• Numbers include operators and trigonometric functions
• Basic arithmetic operations include addition, subtraction, multiplication, division, and parentheses
• Command for addition A+B, A-B for subtraction

Multiplication Notes

• Inner dimensions of multiplication operand must match
• Division can be performed using division operator
• Operator Precedence Rules are similar to mathematics
• Parenthesis, multiplication/division, addition and subtraction

Operator Types

• Unary operators operate on a single value
• Binary operators operate on two values
• Some operators can be unary or binary depending on their usage (+,-)
• Common operators include +, -, *, /, and ^(exponentiation)

Nester Parenthesis

• Inside parenthesis are evaluated first
• In the expression 5-(6*(4+2)) the addition is performed first

Relational Expressions

• Expressions are either true or false, called Relational or Boolean expression.

Operator Expressions

• Use both relational and logical operators
• Equality operator should be two consecutive equal signs (==)
• Logical value 1 is true and 0 is false
• Built in true and false, equivalent logical(1) and logical(0)

Mathematical Operations

• Can be used on the resulting 1 or 0 from expressions
• Logical operators must operation on Boolean operands
• || means Or
• && means and
• ~ means not
• Operator for Or, result is true if either or both operands are true, false only if both are false
• Operator for And, the result is true only if both operands are true, false if either or both are false

Short-Circuit Operators

• || and && are short-circuit operators
• If the expression can be determined by the first part, the second part is not evaluated
• xor function, exclusive or function, returns logical true if only argument it true, otherwise false

Operator Precedence Rules

• Parentheses, exponentiation, negation, multiplication/division, addition/subtraction, relational, logical (&&, xor, ||), and assignment, in that order of precedence