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Presentation On
“Application Of Matrices”
Presented By
MD RASED KHAN
ID: 22702031
SESSION:2021-22
Under The Guidance Of
Mohammad Jahed Hasan
Lecturer, dept. of EEE
Department of Electrical and Electronics Engineering
University Of Chittagong
Some basic methods of Matrix
Addition
Subtraction
Multiplication
Inverse
Transpose
 Eigen vectors: Vectors that are only scaled by matrices are called
Eigen vectors of that corresponding matrix.
 Eigen value: How much the vector is scaled by is called the eigenvalue.
2x + y + 2z = 0
2x – y + z = 10
X + 3y – z = 5
Linear Equation solving:
2 1 2
3 -1 1
1 3 -1
X
Y
z
0
10
5
𝐴𝑥 = 𝐵
Circuit solving:
Humans
150
Covid
positive
150
20%
10%
Virus spread prediction:
Humans: .8(150) + .1(150) = 135
Covid positive : .2(150) + .9(150) = 165
Humans
135
Covid
positive
165
20%
10%
Virus spread prediction:
Humans: .8(135) + .1(165) = 125
Covid positive : .2(135) + .9(165) = 175
Covid
positive
If we represent those percentages as matrices
then we get a linear equation:
h and z are initial values of humans and covid positive population
And h and z are population after an hour.
𝑓 𝑓
Google page rank Algorithm:
PageRank (PR) is an algorithm used by Google
Search to rank web pages in their search engine results.
It is named after both the term "web page” and
co-founder Larry Page.
The spectrum of eigenvalues of the Google matrix of University
of Cambridge from Fig.1 at α = 1, blue points show eigenvalues
of isolated subspaces, red points show eigenvalues of core
component.
Fig.1
Image processing:
Blurred image
Box Blur
If we take the standard arithmetic mean of the component matrices R, G and B
from a color image A ,we will get a gray scale version of the image (non-integer
values are rounded to the nearest integer)
Before After
Box Blur
Edge detection
Matrices in Cryptography:
1.Encode a message using matrix multiplication.
2.Decode a coded message using the matrix inverse and matrix
multiplication
Some common applications of matrices include:
 Computer Graphics
 Statistics and Data Analysis
 Economics and Finance
 Machine Learning and Artificial
Intelligence
 Network Analysis
 Optimization
 Neaural networks
Thank You

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Application of Matrices in real life. Presentation on application of matrices

  • 1. Presentation On “Application Of Matrices” Presented By MD RASED KHAN ID: 22702031 SESSION:2021-22 Under The Guidance Of Mohammad Jahed Hasan Lecturer, dept. of EEE Department of Electrical and Electronics Engineering University Of Chittagong
  • 2. Some basic methods of Matrix Addition Subtraction Multiplication Inverse Transpose
  • 3.  Eigen vectors: Vectors that are only scaled by matrices are called Eigen vectors of that corresponding matrix.  Eigen value: How much the vector is scaled by is called the eigenvalue.
  • 4. 2x + y + 2z = 0 2x – y + z = 10 X + 3y – z = 5 Linear Equation solving: 2 1 2 3 -1 1 1 3 -1 X Y z 0 10 5 𝐴𝑥 = 𝐵
  • 6. Humans 150 Covid positive 150 20% 10% Virus spread prediction: Humans: .8(150) + .1(150) = 135 Covid positive : .2(150) + .9(150) = 165
  • 7. Humans 135 Covid positive 165 20% 10% Virus spread prediction: Humans: .8(135) + .1(165) = 125 Covid positive : .2(135) + .9(165) = 175
  • 8. Covid positive If we represent those percentages as matrices then we get a linear equation: h and z are initial values of humans and covid positive population And h and z are population after an hour. 𝑓 𝑓
  • 9. Google page rank Algorithm: PageRank (PR) is an algorithm used by Google Search to rank web pages in their search engine results. It is named after both the term "web page” and co-founder Larry Page. The spectrum of eigenvalues of the Google matrix of University of Cambridge from Fig.1 at α = 1, blue points show eigenvalues of isolated subspaces, red points show eigenvalues of core component. Fig.1
  • 11. If we take the standard arithmetic mean of the component matrices R, G and B from a color image A ,we will get a gray scale version of the image (non-integer values are rounded to the nearest integer)
  • 13. Matrices in Cryptography: 1.Encode a message using matrix multiplication. 2.Decode a coded message using the matrix inverse and matrix multiplication
  • 14. Some common applications of matrices include:  Computer Graphics  Statistics and Data Analysis  Economics and Finance  Machine Learning and Artificial Intelligence  Network Analysis  Optimization  Neaural networks