APPLICATION OF MATRICES

Md: Mahmudle HassanDepartment of Civil Eng.At Daffodil International Universityhttps://www.facebook.com/MHMMEHEDI12

Website: https://needtune.blogspot.com

Matrices

A rectangular arrangement of numbers in rows and columns.

It is the Combination of linear equation. It is Represented by these symbols:

[], ||,()

EXAMPLE

197324

)a

293705

)b

381) c

5123481097

)d

row

column

column

row

row

column

column

row

DIMENSIONS OF THE MATRIX

Row (m)

234012

Column(n)

A matrix with m rows and n columns is called a matrix with dimensions m x n

(# no. of row) x ( # no. of column) This is a 2 X 3 matrix

DIMENSIONS OF THE MATRIX :

Types of Matrices

1. Row matrices – A matrices which has only one row called row matrices e.g.-

[123]1*3 2. Column matrices – A matrices which has only one column

is called column matrices e.g. –

 Null matrix is a matrix with all its entries being zero.

Null matrices

123456789൩3∗3

Square matrices

No of rows = No of column

A square matrices who’s main diagonal is ascent value ‘1’ and each of the other element is ‘0’

Identity matrices

100010001൩3∗3 , ቂ1001ቃ2∗2, ሾ1ሿ1∗1

A square matrices all of who’s element expect those in the leading diagonal are ‘0’

Diagonal matrices

A diagonal matrices in which all the elements of main diagonal is same called scalar matrices.

Scalar matrices

3*3

There are two types triangular matrices ---1.Upper triangular: All the below elements are ‘0’.

2.Lower triangular: All the above elements are ‘0’

Triangular matrices

123045006൩3∗3

100230456൩3∗3

A matrices obtained by inter changing the rows and columns of a matrices.

It is denoted by A’ , AT

Transpose Matrices

A⇒123456789൩3∗3 AT ⇒ 147258369൩3∗3

Cryptography is the process of encrypting data so that third party can’t read it and privacy can be maintained.

It was started with the TV cable industries where even people who were not the customer could watch the TV programs

Application of matrix

Videocipher encryption system was invented which would convert signals into digital form i.e. encrypt it, and the data were send over the satellite.

Application of matrix

Since we are using a 3 by 3 matrix, we break the enumerated message above into a sequence of 3 by 1 vectors:

Note that it was necessary to add a space at the end of the message to complete the last vector.

We encode the message by multiplying each of the above vectors by the encoding matrix.

We represent above vectors as columns of a matrix and perform its matrix multiplication with the encoding matrix

27520

1920

1575

142715

20275

18116

51816

2711514201855972727118202051551616

434110433

Encoding

In geologymatrices are used for taking seismic surveys. They are used for plotting graphs, statistics

and also to do scientific studies in almost different fields.

In Physicsmatrices are applied in the study of electrical

circuits, quantum mechanics and optics. In the calculation of battery power outputs,

resistor conversion of electrical energy into another useful energy, these matrices play a major role in calculations. 

Especially in solving the problems using Kirchoff’s laws of voltage and current, the matrices are essential.

First, write a numerical value for each letter i.e. A=1, B=2, and Z=26, and space=27.

The data should be placed in matrix form i.e. in 2x1 or 3x1 matrix form.

How to encrypt data?Encryption process

The data should be multiplied by given encoding matrix.

Then, write the answer (value after multiplying) in linear form. How to encrypt data? Encryption Process

In computer based applicationsmatrices play a vital role in the projection of

three dimensional image into a two dimensional screen, creating the realistic seeming motions. 

Stochastic matrices and Eigen vector solvers are used in the page rank algorithms which are used in the ranking of web pages in Google search. 

The matrix calculus is used in the generalization of analytical notions like exponentials and derivatives to their higher dimensions. 

One of the most important usages of matrices in computer side applications are encryption of message codes. 

Matrices and their inverse matrices are used for a programmer for coding or encrypting a message. 

In computer based applications

Other Use of Matrix Matrices are used in representing the real world data’s like the traits of people’s

population, habits, etc.  They are best representation methods for plotting the common survey things.

•    Matrices are used in calculating the gross domestic products in economics which eventually helps in calculating the goods production efficiently. 

•    Matrices are used in many organizations such as for scientists for recording the data for their experiments.

  •    In robotics and automation, matrices are the base elements for the robot

movements.  The movements of the robots are programmed with the calculation of matrices’

rows and columns.  The inputs for controlling robots are given based on the calculations from

matrices. 

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