Application of matrices in real life and matrix

presentation on Matrix and its application

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1. MATRIX Presentation by : DD MU @darsh921 Prepared By: Darsh Patel DD921921 B.tech 2 nd Semester , MU UNIVERSITY

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3. A LITTLE BIT OF HISTORY The history of matrices goes back to ancient times , but the term “Matrix” was not applied to the concept till 1850 Matrix is the Latin word for womb and it retains that sense in English It can also mean more generally any place where something is formed or produced A LITTLE BIT OF HISTORY @darsh921

4. A LITTLE BIT OF HISTORY He was instrumental in proposing a matrix concept independent of equation systems. In 1858 Cayley published his  A memoir on the theory of matrices which he proposed and demonstrated the  Cayley-Hamilton theorem . In linear algebra, the Cayley–Hamilton theorem states that every square matrix over a commutative ring satisfies its own characteristic equation. @darsh921

5. Row Matrix Column Matrix Null matrix Square Marix Diagonal Matrix Upper triangular matrix Lower triangular matrix Symmetric matrix Anti-Symmetric matrix TYPE OF MATRIX

6. Use of Matrices In Computer Graphics APPLICATION Earlier architecture, cartoons, automation were done by hand drawings but nowadays they are done by using computer graphics . Square matrices very easily represent linear transformation of objects. In Graphics, digital image is treated as a matrix to start with Matrixoperations such as translation, rotation and sealing are used in graphics. For transformation of a point we use the equation EXAMPLE : @darsh921

7. Use of Matrices in Cryptography Cryptography is the technique to encrypt data so that only the relevant person can get the data and relate information. One type of code, which is extremely difficult to break, makes use of a large matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. This first matrix, used by the sender is called the encoding matrix and its inverse is called the decoding matrix , which is used by the receiver. EXAMPLE : @darsh921

8. A LITTLE BIT OF HISTORY Use of Matrices in Wireless ommunication Matrices are used to model the wireless signals and to optimize them. Matrices help in processing and representing digital images. important part of the telecommunication industry. Sensor array signal processing focuses on signal enumeration and source location applications and presents a huge importance in many domains such as radar signals and underwater surveillance. EXAMPLE : @darsh921

9. Use of Matrices in Robotics In robotics and automation, matrices are the base elements for the robot movements The movements of the robots are programmed in MATLAB using matrix pencil method. Matrices are used for movements in Robot Arms. ROBOTICS EXAMPLE : @darsh921

10. Use of Matrices in Chemical In chemistry we use matrix methodology to balance the chemical equations Initially we transform the chemical equations into the matrices form. Then we apply Gauss Jordon method to calculate the chemical reactions  aFeCl2 + bNa3(PO4) cFe3(PO4)2 + dNaCl Fe: (1×a) + (0×b) –(3×c) = 0×d Cl: (2 × a)+(0×b )+(0 × c) = 1 × d Na: (0 × a)+(3 × b)+(0× c) = 1 × d (PO4): (0×a)+(1×b)–(2 × c) = 0 × d    EX: @darsh921

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