Applications of linear algebra in computer science

Applications of linear algebra in computer science
2nd semester math

1. WELCOME TO our presentation on “Application of linear algebra in cse ” We are “RAINBOW WARRIORS”

2. Name: ID: MD. Atikur Rahman 181-15-2024 MD. Najmus Shakib 181-15-1913 MD. Aminul Islam 181-15-1888 MD. Rasel Ahmed 181-15-2060 Jakirul Hasan 172-15-1615 Group Name : RAINBOW WARRIORS 1 Page

3. Introduction When you take a digital photo with your phone or transform the image in Photoshop, when you play a video game or watch a movie with digital effects, when you do a web search or make a phone call, you are using technologies that build upon linear algebra. Linear algebra in turn is built on two basic elements, the matrix and the vector. 2 Page

4. History of Linear Algebra The study of linear algebra first emerged from the introduction of determinants. Determinants were considered by Leibniz in 1693, and subsequently, in 1750, Gabriel Cramer used them for giving solutions of linear systems, now called Cramer's Rule. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination. The study of matrix algebra first emerged in England in the mid-1800s. Linear algebra first appeared in American graduate textbooks in the 1940s and in undergraduate textbooks in the 1950s 3 Page

5. • Linear algebra is vital in multiple areas of computer science because linear equations are so easy to solve. • It converts large number of problems to matrix and thus we solve the matrix. Why Linear Algebra is important ? 4 Page

6. Uses of Linear Algebra in CSE Linear Algebra in computer science can broadly divided into two categories: Here you're dealing with 2-, 3-, or 4-dimensional vectors and you're concerned with rotations, projections, and other matrix operations that have some spatial interpretation. This is the kind of linear algebra that comes up, for example, in computer graphics and physics simulations. Linear Algebra for spatial quantities. 5 Page

7. Here you're dealing with vectors in high-dimensional spaces that have no particular spatial interpretation and you're interested in matrix decompositions and so on. This domain includes signal processing, statistical machine learning, and compression. 2) Linear Algebra for statistics. 6 Page

8. Linear Algebra in Network Models Determine the currents I1, I2, and I3 for the following electrical network: 7 Page

9. By Kirchhoff’s Law: 8 Page

10. Linear Algebra in Cryptography Encryption and decryption require the use of some secret information, usually referred to as a key. Example Let the message be “PREPARE TO NEGOTIATE” We assign a number for each letter of the alphabet. Thus the message becomes: 9 Page

11. Since we are using a 3 by 3 matrix, we break the enumerated message above into a sequence of 3 by 1 vectors: By multiplying encoding matrix to this matrix we will encrypt the msg. 10 Page

12. Now to decrypt the msg we have to multiply this matrix to Inverse of encoding matrix • The inverse of this encoding matrix, the decoding matrix, is: • Multiplying again by this matrix we will get our Msg. 11 Page

13. Importance of Linear Algebra in various category Very important in Computer Vision for: Camera modeling; Epipolar geometry; Calibration and self-calibration; Pose estimation; Structure-from-motion; And many other things. 12 Page

14. Very important in Machine Learning. For example : Dimensionality reduction; (e.g. Principal component analysis) Clustering; Classification; Prediction; Recommender systems ( e.g Collaborative filtering) etc.. 13 Page

15. Page 14 Matrix in Neural Network

16. Linear Algebra is crucial to: Audio, video and image compression, including MP3, JPEG and MPEG video. Modulation and coding, including convolutional codes and Wi-Fi, Gigabit Ethernet, HDTV and the GPS. Signal processing, including the Fast Fourier Transform and autotune! Statistics and machine learning, including something as far a field like automated trading in the financial markets 15 Page

17. In computer graphics every element is represented by a MATRIX. Linear Algebra Computer Graphics All images can be represented in matrix format. 16 Page

18. Page 17 Linear Algebra in video games Linear algebra is the study of vectors. If your game involves the position of an on-screen button, the direction of a camera, or the velocity of a race car, you will have to use vectors. The better you understand linear algebra, the more control you will have over the behavior of these vectors. In games, vectors are used to store positions, directions, and velocities. Here are some 2-Dimensional examples: The position vector indicates that the man is standing two meters east of the origin, and one meter north. The velocity vector shows that in one minute, the plane moves three kilometers up, and two to the left. The direction vector tells us that the pistol is pointing to the right.

19. Conclusion There are so many application of Linear Algebra in Computer Science. From simple circuit solving to large web engine algorithms. The heart beat of computer science is in linear algebra especially in the generation and formation of computer coding schemes . That's the study of matrices especially identity matrices under linear algebra is key to computer coding schemes generation and formation unlike what we have in computer engineering. These are programming primitives normally encapsulated into programming languages and translators design. 18 Page

20. Therefore linear algebra is a course in mathematics which is a subfield in theoretical computer science. Of course linear algebra is also useful in secondary programming, like in computer graphics, database systems and IP address design, etc. 19 Page

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