Presentation on application of matrix

Application of matrix
1. Encryption, its process and example
2. Decryption, its process and example
3. Seismic Survey
4. Computer Animation
5. Economics
6. Other uses...

1. Presentation On Application Of Matrix Prepared By: Prerana Bhattarai 139/13 BBA 2 nd Semester ‘B’

2. 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 So, Videocipher encryption system was invented which would convert signals into digital form i.e. encrypt it, and the data were send over the satellite. The Videocipher box would decrypt the signal and those satellite dish owner who had Videocipher box would receive the decrypted signal i.e. the original signal before encryption. In matrix same thing can be done. Application of Matrix

3. 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. 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

4. The encoding matrix be Then, assign numeric value for “SUBMIT H ER YOUR PLANS” i.e. S=19, U=21, B=2, M=13, I=9, T=20, space=27, H=8, E=5, R=18, space=27, Y=25, O=15, U=21, R=18, space=27, P=16, L=12, A=1, N=14, S=19     Example: Let take the message SUBMIT ME YOUR PLAN :     S U B M I T H E R Y O U R P L A N S 19 21 2 13 9 20 27 8 5 18 27 25 15 21 18 27 16 12 1 14 19

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

6. The message should be encoded by multiplying the above 3x1 matrix by the given encoding matrix. 19 13 27 18 15 27 1 21 9 8 27 21 16 14 2 20 5 25 18 12 19   This gives, 17 -7 22 -7 -3 15 -18 21 9 8 27 21 16 14 -19 11 -3 -2 -3 -4 5

7. The columns of this matrix give the encoded message. The message is transmitted in the following linear form 17, 21, -21, -7, 9, -9, 22, 8, -8, -7, 27, -27, -3, 21, -21, 15, 16, -16, -18, 14, -14

8. The encrypted number should be written in matrix form. The inverse of the encoding matrix should be found. Multiply the inverse encoding matrix, i.e. decoding matrix with the encrypted number. Write the answer in linear form . Assign 1=A, 2=B and so on and also 27=space. Decryption Process

9. The inverse of the encoding matrix should be taken out such as:  

10. Thus , to decode the message, perform the matrix multiplication   and get the matrix   17 -7 22 -7 -3 15 -18 21 9 8 27 21 16 14 -19 11 -3 -2 -3 -4 5 19 13 27 18 15 27 1 21 9 8 27 21 16 14 2 20 5 25 18 12 19

11. The columns of this matrix, written in linear form, give the original message : S U B M I T H E R Y O U R P L A N S 19 21 2 13 9 20 27 8 5 18 27 25 15 21 18 27 16 12 1 14 19

12. Many geologists make use certain  types of matrices for seismic surveys. The seismic survey is one form of geophysical survey that aims at measuring the earth’s (geo-) properties by means of physical (-physics) principles such as magnetic,  electric , gravitational, thermal, and elastic theories. Seismic Surveys

13. Matrices are used to calculate gross domestic product in economics, and help in calculation for producing goods more efficiently. It is seen that through input-output analysis that is used in matrix a researcher can get information about what level of output should be of each industry at the existing technology. In economics

14. Matrix transforms are very useful within the world of computer graphics. Software and hardware graphics processor uses matrices for performing operations such as scaling, translation, reflection and rotation. Computer Animations

15. Matrices are very  useful for organization, like for scientists who have to record the data from their experiments if it  includes numbers. In engineering, math reports are  recorded using matrices. And in architecture,  matrices are used with computing. If needed, it will  be very easy to add the data together, like with matrices in mathematics. Other uses…

16. ANY QUESTIONS?