Lesson 01: Introduction to MATLAB

What is MATLAB?

The name MATLAB stands for "MATrix LABoratory" and was originally designed as a tool for doing numerical computations with matrices and vectors. It has since grown into a high-performance language for technical computing. MATLAB, integrating computation, visualization, and programming in an easy-to-use environment, allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Typical uses include:

Math and Computation
Modeling and Simulation
Data Analysis and Visualization
Application Development
Graphical User Interface development

Getting Started

Window Layout

MATLAB development IDE can be launched from the icon created on the desktop. The main working window in MATLAB is called the desktop. When MATLAB is started, the desktop appears in its default layout:

MatLab MainScreen

The following tools are managed by MATLAB desktop, although not all of them appear by default when you first start

Current Folder - This panel allows you to access the project folders and files.
Command Window - This is the main area where commands can be entered at the command line.It is indicated by the command prompt (>>).
Workspace - The workspace shows all the variables created and/or imported from files.
Command History - This panel shows or rerun commands that are entered at the command line.

By default, the Command History window closes after a statement is selected or the Esc key is pressed. To keep the Command History window open, in the Command History window, click and then select either Detach or Dock. If the Command History window is closed while detached or docked, go to the Home tab, and in the Environment section, click Layout. Then, under Show, click Command History and select either Docked or Popup.

1.1 MATLAB Basics

MATLAB Basics

Variables
Matrices and Vectors

Variables
Matrices and Vectors

Variables

Variables

MATLAB does not require a command to declare variables. A variable is created simply by directly allocating a value to it. All variables are created with double precision unless specified and they are matrices.

>> v = 3
v =
3

After these statements, the variables are 1x1 matrices with double precision.

>> 23 + 18 # no declarations needed
ans =
41

>> product = 18 * 32.64 # mixed data type
product =
5.875200000000000e+02

>> product = 18 * 555.24; # semi-colon suppresses output of calculation's result
>> product
product =
9.994320000000000e+03

MATLAB Variable Names

Variable names are CASE SENSITIVE.
Variable names can contain up to 63 characters (as of MATLAB 6.5 and newer).
Variable names must start with a letter followed by letters. digits, and underscores ( _ ).
MATLAB has several keywords that cannot be used as programmer-defined variable names.

The following table provides a list of keywords. The list of keywords can be found by entering the command "iskeyword" on the Command Window.

break	case	catch	classdef	continue
else	elseif	end	for	function
global	if	otherwise	parfor	persisyent
return	spmd	switch	try	while

Special Variables and Constants

Command	Description
ans	Temporary variable containing the most recent answer. If you do not assign an output variable to an expression, MATLAB automatically stores the result in ans.
eps	This variable name is short for “epsilon”. It is the smallest difference between two numbers that can be represented on the computer. (Smallest incremental number)
i, j	The imaginary unit $\sqrt { - 1}$
inf	Infinity. Calculations like n/0, where n is any non-zero real value, result in inf.
NaN	Not-a-Number, indicates an undefined numerical result. Expressions like *0/0* and inf/inf result in a *NaN, as do arithmetic operations involving a NaN. n/0, where n is complex, also returns NaN*.
pi	The number $\pi$ ( = 3.1415926535897...)
realmin	The smallest usable positive real number.
realmax	The largest usable positive real number.
computer	Computer type.
version	MATLAB version string.
clock	This special variable contains the current date and time in the form of a 6-element row vector containing the year, month, day, hour, minute, and second.
date	Contains the current data in a character string format, such as 24-Nov-1998.

Here are several examples that use these values in MATLAB expressions.

>> x = 2 * pi;
>> A = [3+2i 7-8i];
>> tol = 3 * eps;

1.2 MATLAB Operators and Special Characters

Arithmetic Operators

Arithmetic Operators

Symbol	Role
+	Addition
+	Unary plus
-	Subtraction
-	Unary minus
*	Matrix multiplication
/	Matrix right division
^	Matrix power

Symbol	Role
.*	Element-wise multiplication
.\	Element-wise left division
.^	Element-wise power
.'	Transpose
'	Complex conjugate transpose

Array Operations
Element-wise Operations

Array Operations
Element-wise Operations

Array Operations

Array Operations

There are two types of arithmetic operators in MATLAB:

Matrix arithmetic operators, which are governed by the rules of linear algebra.
Vector arithmetic operators, which are performed element-wise.

Matrix Operations

Operation	Role Played
A + B	Scalar and array addition
A - B	Scale and array subtraction
A * B	Scale multiplication and multiplication in matrix algebra. (The number of columns in A must equal the number of rows in B.)
A / B	Right division: scale division and division in matrix algebra. A / B = A inv(B)* where A and B are matrices
A \ B	Left division. A \ B = inv(A) B*, where A and B are matrices.
A ^ b	Scalar exponentiation and matrix exponentiation in matrix algebra (A^b)
A'	Transpose

Element-wise Operations

Element-wise Operations

Evaluated element by element

Operation	Role Played
*a . b**	Element-by-element multiplication of a and b. Both arrays must be the same shape, or one of them must be a scalar.(dot multiply or dot star).
a ./ b	Element-by-element right division of a and b. Both arrays must be the same shape, or one of them must be a scalar. A ./ B = [A(i,j) / B(i,j)], where A and B are arrays [dim(A) = dim(B)]
a .\ b	Element-by-element left division of a and b Both arrays must be the same shape, or one of them must be a scalar. A .\ B = [B(i,j) / A(i,j)], where A and B are arrays [dim(A) = dim(B)]
a .^ b	Element-wise power. Both arrays must be the same shape, or one of them must be a scalar.(dot power or dot caret). A .^ B = [a(i,j)^b(i,j)], for arrays A and B
a.'	Array transpose (non-conjugated transpose)

Example: Array Operations

Example: Element-Wise Operations

When you multiply a scalar times an array you may use either operator ( * or .* ), but when you multiply two arrays together they mean something quite different.
Unfortunately, when you divide a scalar by an array you still need to use the ./ syntax because the / means taking the matrix inverse to MATLAB. As a general rule, unless you specifically are doing problems involving linear algebra (matrix mathematics), you should use the dot operators.

Special Characters

Special Characters

Symbol	Description
@	Name: At symbol Uses: Function handle construction and reference Calling superclass methods The @ symbol forms a handle to either the named function that follows the @ sign, or to the anonymous function that follows the @ sign. You can also use @ to call superclass methods from subclasses. Examples: at Symbol
.	Name: Period or dot Uses: Decimal point Element-wise operations Structure field access Object property or method specifier The period character separates the integral and fractional parts of a number, such as `3.1415`. MATLAB operators that contain a period always work element-wise. The period character also enables you to access the fields in a structure, as well as the properties and methods of an object. Examples: dot Symbol
...	Name: Dot dot dot or ellipsis Uses: Line continuation Three or more periods at the end of a line continue the current command on the next line. If three or more periods occur before the end of a line, then MATLAB ignores the rest of the line and continues to the next line. This effectively makes a comment out of anything on the current line that follows the three periods. Examples: ellipsis Symbol
,	Name: Comma Uses: Separator Use commas to separate row elements in an array, array subscripts, function input, and output arguments, and commands entered on the same line. Examples: comma Symbol
:	Name: Colon Uses: Vector creation Indexing For-loop iteration Use the colon operator to create regularly spaced vectors, index into arrays, and define the bounds of a for loop. Examples: colon Symbol
;	Name: Semicolon Uses: Signify end of row Suppress output of code line Use semicolons to separate rows in an array creation command, or to suppress the output display of a line of code. Examples: Semicolon Symbol
( )	Name: Parentheses Uses: Operator precedence Function argument enclosure Indexing Use parentheses to specify the precedence of operations, enclose function input arguments, and index into an array. Examples: Parentheses Symbol
[ ]	Name: Square brackets Uses: Array construction Array concatenation Empty matrix and array element deletion Multiple output argument assignment Square brackets enable array construction and concatenation, creation of empty matrices, deletion of array elements, and capturing values returned by a function. Examples: Square brackets Symbol
{ }	Name: Curly brackets Uses: Cell array assignment and contents Use curly braces to construct a cell array, or to access the contents of a particular cell in a cell array. Examples: Curly brackets Symbol
%	Name: Percent Uses: Comment Conversion specifier The percent sign is most commonly used to indicate nonexecutable text within the body of a program. This text is normally used to include comments in your code. Some functions also interpret the percent sign as a conversion specifier. Two percent signs, %%, serve as a cell delimiter as described in Code Sections. Examples: Percent Symbol
%{ %}	Name: Percent curly bracket Uses: Block comments The %{ and %} symbols enclose a block of comments that extend beyond one line. Examples: Percent curly bracket Symbol
!	Name: Exclamation point Uses: Operating system command The exclamation point precedes operating system commands that you want to execute from within MATLAB Not available in MATLAB Online. Examples: Exclamation point Symbol
?	Name: Question mark Uses: Metaclass for MATLAB class The question mark retrieves the meta.class object for a particular class name. The ? operator works only with a class name, not an object Examples: Question mark Symbol
' '	Name: Single quotes Uses: Character array constructor Use single quotes to create character vectors that have class char. Examples: Single Quotes Symbol
" "	Name: Double quotes Uses: String constructor Use double quotes to create string scalars that have class string Examples: Double Quotes Symbol
	Name: Space character Uses: Separator Use the space character to separate row elements in an array constructor, or the values returned by a function. In these contexts, the space character and comma are equivalent. Examples: Space Character Symbol
enter	Name: Newline character Uses: Separator Use the newline character to separate rows in an array construction statement. In that context, the newline character and semicolon are equivalent. Examples: Newline Character Symbol
~	Name: Tilde Uses: Logical NOT Argument placeholder Use the tilde symbol to represent logical NOT or to suppress specific input or output arguments.. Examples: Tilde Symbol
=	Name: Equal Sign Uses: Assignment Use the equal sign to assign values to a variable. The syntax B = A stores the elements of A in variable B. Examples: Equal Sign Symbol The = character is for assignment, whereas the == character is for comparing the elements in two arrays.
< &	Name: Left angle bracket and ampersand Uses: Specify superclasses Specify one or more superclasses in a class definition Examples: Left Angle Bracket and Ampersand Symbol
. ?	Name: Dot question mark Uses: Specify fields of name-value structure When using function argument validation, you can define the fields of the name-value structure as the names of all writeable properties of the class. Examples: Equal Sign Symbol

String and Character Formatting

Some special characters can only be used in the text of a character vector or string. You can use these special characters to insert newlines or carriage returns, specify folder paths, and more.

Use the special characters in this table to specify a folder path using a character vector or string.

Operation	Role Played
/ \	Name: Slash and Backslash Uses: File or folder path separation In addition to their use as mathematical operators, the slash and backslash characters separate the elements of a path or folder. On Microsoft Windows based systems, both slash (/) and backslash (\) have the same effect. On The Open Group UNIX based systems, you must use slash only. Examples: Slash and Backslash Symbol
..	Name: Dot dot Uses: Parent folder Two dots in succession refers to the parent of the current folder. Use this character to specify folder paths relative to the current folder. Examples: Dot Dot Symbol
*	Name: Asterisk Uses: Wildcard character In addition to being the symbol for matrix multiplication, the asterisk * is used as a wildcard character. Wildcards are generally used in file operations that act on multiple files or folders. MATLAB matches all characters in the name exactly except for the wildcard character *, which can match any one or more characters. Examples: Asterisk Symbol
@	Name: At symbol Uses: Class folder indicator An @ sign indicates the name of a class folder. Examples: At Symbol (folder)
+	Name: Plus Uses: Package directory indicator A + sign indicates the name of a package folder. Examples: Plus Symbol

1.3 Math Functions

Practice Exercises

Exe 1: MATLAB Expressions

Exe 2: ans Variable

Exe 3: Operators

Exe 4: Math Function

Exe 5: Valid MATLAB variable names

Operation	Role Played
<	Less than
<=	Less than or equal to
>	Greater than
>=	Great than or equal to
==	Equal to
~=	Not equal to

functions	Role Played
xor(A,B)	Logical Exclusive OR.
or (A,B)	Logical OR.
and (A,B)	Logical AND.
not (A)	Logical NOT.
any (X)	Returns 1 if any element of X is true or non-zero. any function operates columnwise on matrices.
all (X)	Returns 1 if all elements of X are true or non-zero. all operates columnwise on matrices.
isnan (X)	Returns 1 at each NaN in X.
isinf (X)	Returns 1 at each infinity in X.
isfinite (X)	Returns 1 at each finite value in X.
isempty (X)	Returns 1 if X is an empty array. An empty array has no elements.

functions	Role Played	MATLAB Example
abs (x)	Finds the absolute value of x.	>> abs (-3) ans = 3
sqrt (x)	Finds the square root of x.	>> sqrt (85) ans = 9.2195
nthroot (x,n)	Finds the real n_th root of x. This function will not return complex results.	>> nthroot(-2,3) ans = -1.2599
sign (x)	Returns a value: -1: if (x < 0) 0: if (x == 0) 1: if (x > 0)	>> sign (-8) ans = -1
rem (x, y)	Computes the remainder of x / y.	>> rem (25, 4) ans = 1
exp (x)	Computes the value of *e^x, where e is the base for natural logarithms, or approximately 2.7183*.	>> exp (10) ans = 2.2026e+04
log (x)	Computes *ln(x)*, the natural logarithm of x (to the base e).	>> log (10) ans = 2.3026
log10 (x)	Computes log₁₀ (x), the common logarithm of x (to the base 10).	>> log10(10) ans = 1

functions	Role Played
sin (x)	Finds the sine of x when x is expressed in radians, sin(x).
cos (x)	Finds the cosine of x when x is expressed in radians, cos(x).
tan (x)	Finds the tangent of x when x is expressed in radians, tan(x).
asin (x)	Finds the arcsine sin^-1(x), or inverse sine, of x, where x must be between -1 and 1.
sinh (x)	Finds the hyperbolic sine of x when x is expressed in radians, sinh(x).
asinh (x)	Finds the inverse hyperbolic sin of x, sinh^-1(x).
sind (x)	Finds the sin of x when x is expressed in degrees, sin(xº).
asind (x)	Finds the inverse sin of x and reports the result in degrees, sin^-1(x).

Operation	Role Played
~	logical NOT
&	logical AND
\|	logic OR

Lesson 01: Introduction to MATLAB

What is MATLAB?

Getting Started

Window Layout

1.1 MATLAB Basics

Variables

MATLAB Variable Names

Special Variables and Constants

Matrices and Vectors

1.2 MATLAB Operators and Special Characters

Arithmetic Operators

Array Operations

Matrix Operations

Element-wise Operations

Example: Array Operations

Example: Element-Wise Operations

Relational Operators

Logical Operators/Functions

Special Characters

Examples: at Symbol

Examples: dot Symbol

Examples: ellipsis Symbol

Examples: comma Symbol

Examples: colon Symbol

Examples: Semicolon Symbol

Examples: Parentheses Symbol

Examples: Square brackets Symbol

Examples: Curly brackets Symbol

Examples: Percent Symbol

Examples: Percent curly bracket Symbol

Examples: Exclamation point Symbol

Examples: Question mark Symbol

Examples: Single Quotes Symbol

Examples: Double Quotes Symbol

Examples: Space Character Symbol

Examples: Newline Character Symbol

Examples: Tilde Symbol

Examples: Equal Sign Symbol

Examples: Left Angle Bracket and Ampersand Symbol

Examples: Equal Sign Symbol

String and Character Formatting

Examples: Slash and Backslash Symbol

Examples: Dot Dot Symbol

Examples: Asterisk Symbol

Examples: At Symbol (folder)

Examples: Plus Symbol