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

Application of matrices in real life. how matrices dominate our real life? how to relate matrices in real life problem and solve those problems . matrices on engineering sector. some interesting examples are included. this is the presentation slide.
department of Electrical and Electronic Engineering , University of Chittagong.

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: 1 2 -1 1 1 3 -1 X Y z 10 5  

5. Circuit solving:

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.    

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

10. Image processing: Blurred image Box Blur

11. I f 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)

12. Before After Box Blur Edge detection

13. Matrices in Cryptography: Encode a message using matrix multiplication. 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