## Matrix and Vectors Construction

In this tutorial you will learn:

1.  Matrix and vector Construciton.
2. Zero Matrix
3. Ones Matrix
4. Identity Matrix
5. Linerally spaced vectors
6. Logarithmically spaced vectors

So lets get started!

# Matrices

Matrices in Matlab are one of the prime reasons for user to stick around.  It is called MATrixLABoratory for a reason. Otherwise, there are better alternatives when it comes to other features.

Now, a matrix has rows and columns. Kinda looks like this 😀

So, how do we make this sucker in Matlab?

Like this!

Or, you can go like this to save space:

m = [ 1, 1, 0;0, 1, 0;0, 0, 1];

A few more matrices are:

Column Vector:  m = [1;2;3;4]

Row vector: m = [1,2,3,4]

A 2×3 vector m = [1,2 ; 3,4 ; 5,6]

# Special Matrices

I am calling them special matrices because these matrices have a special property which can be exploited for our purpose:

### Zero Matrix

These matrices have nothing but zeroes in them. They are declared like:

zeros(20, 7)

### Ones Matrix

Contrary to Zero Matrix, Ones matrix have every element set as “1”. These matrices are declared like,

ones(4, 20)

### Identity Matrix

An identity matrix has ones in the diagonal while zeroes on every other element. It is made like this:

eye(10)

eye(4, 6)

### Linearly Spaced Vector

This command creates an evenly spaced vector between two numbers. The format is,

linspace(startingNumber, endingNumber, numberOfPoints)

e.g.

linspace(1, 10, 10)

### Logarithmically spaced vectors

This command creates Logarithmically spaced vector between two numbers. The format is,

logspace(RangeStartingfrom 10^THISNUMBER, RangingEndingAt 10^THISNUMBER, numberOfLogarithmicallyPoints)

So, logspace(1, 5, 10); will mean that we wish to create a logarithmically spaced vector of 10 points between 10^1 and 10^5

This just about covers the basics of Matrix and vectors. You have learnt the basics and construction of some of the most commonly used matrices in Matlab. Now, you have enough understanding to proceed towards matrix operations and manipulation.

## Variables, Arithmetic operations and Functions in Matlab

In this tutorial I will explain to you how to use variables, perform basic arithmetic operations and usage of some common mathematical functions in Matlab. Lets start right away.

# Creating a simple variable

Creating a variable is very simple. A variable name, an “=” sign and a value. For example, in command window, you would write,

x = 100

Here, we defined a variable x to have a value of 100.

# Basic Arithmetic Operations

Addition, subtraction, multiplication and division is performed by using +, -, *, / operators respectively on a variable. This is shown below:

# Powers

We are going to give power to variables now. It is simple like:

>> x = 4

x =4

>> x^1000

ans =Inf

>> x^100

ans =1.6069e+60

# Squareroot

Root the numbers back to their squares using:

sqrt(x);

sqrt(16);

# Logarithmic Operations

This is done like:

log(105);

log10(105);

log10(pi);

log(-1);

# Trigonometric Ratios

You do it like a boss:

boss = pi;

sin(4*boss/3);

tan(boss*boss);

There are much more functions to get you started on your work in Matlab. But this is enough for this tutorial as I will slowly be advancing towards more advanced and specialized tutorials in the future.

Do comment if you have questions.