- Matlab-Matrix Tutorial
- Matlab-Matrix - Home
- Matlab-Matrix - Introduction
- Matlab-Matrix - Environment Setup
- Matlab-Matrix - Create Matrix
- Matlab-Matrix - Working with Matrices
- Matlab-Matrix - Multiplication
- Matlab-Matrix - Addition
- Matlab-Matrix - Subtraction
- Matlab-Matrix - Matrix Determinant
- Matlab-Matrix - Inverse
- Matlab-Matrix - Trace
- Matlab-Matrix - Rank
- Matlab-Matrix - Transpose
- Matlab-Matrix - Deletion Row & Coloumn
- Matlab-Matrix Useful Resources
- Matlab Matrix - Quick Guide
- Matlab Matrix - Useful Resources
- Matlab Matrix - Discussion

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# Matlab-Matrix - Introduction

MATLAB (matrix laboratory) is a fourth-generation high-level programming language and interactive environment for numerical computation, visualization and programming. It allows matrix manipulations; plotting of functions and data; implementation of algorithms; creation of user interfaces; interfacing with programs written in other languages, including C, C++, Java, and FORTRAN; analyze data; develop algorithms; and create models and applications.

In this tutorial we will focus on Matrix Implementation using MATLAB.

## Matrix

A matrix is a collection of numbers arranged in rows and columns that represents a rectangular array.

An example of matrix with 2 rows and 3 columns is as shown below

## Matrix Dimension

The dimension of a matrix is defined based on the number of rows and columns.

A matrix with 2 rows and 3 columns is said to be 2x3 matrix.

A matrix with 3 rows and 3 columns is said to be 3x3 matrix.

## Matrix in Matlab

In MATLAB, you create a matrix by entering elements in each row as comma or space delimited numbers and using semicolons to mark the end of each row.

### Example

To create a 4x5 matrix, enter the following.

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]

The matrix has 4 rows and 5 columns.

The first row will have values as 1 2 3 4 5

The second row: 2 3 4 5 6

The third row: 3 4 5 6 7

The fourth row: 4 5 6 7 8

### Output

The matrix of size 4x5 will look as follows

a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8

Let us test the matrix creation in MATLAB command window as shown below −

>> a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8] a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 >>

## Referencing the Elements

To reference an element in the mth row and nth column, of a matrix mx, we write the following

mx(m, n);

## Example

To refer to the element in the 2nd row and 5th column, of the matrix a, as created in the last section, we type the following.

>> a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8] a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 >> a(2,5) ans = 6 >>

To get all the elements of the nth column in a matrix , you can make use of A (:,n) where n represents the column no in the matrix.

A(:,n).

### Example

Now, let us create a column vector v, from all the elements of the 4th column of the matrix a. This will be as follows

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; v = a(:,4)

### Output

MATLAB will execute the above statement and return the following result.

>> a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8] a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 >> v=a(:,4) v = 4 5 6 7 >>

You can also select the elements in the mth through nth columns. For this, we write as follows.

a(:,m:n)

### Example

Let us create a smaller matrix by taking the elements from the second and third columns, as shown below −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; a(:, 2:3)

### Output

MATLAB will execute the above statement and return the following result −

>> a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8] a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 >> a(:, 2:3) ans = 2 3 3 4 4 5 5 6 >>

In the same way, you can create a sub-matrix by taking a sub-part of a matrix.

## Example

Let us create a sub-matrix saby taking the inner subpart of a, as given below −

3 4 5 4 5 6

During execution in MATLAB command window, the matrix will be as shown below −

>> a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8] a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 >> sa = a(2:3,2:4) sa = 3 4 5 4 5 6 >>