# Matrix and its Applications

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65 In Mathematics, we have studied different concepts that have various applications in our real-life activities. One such concept that has a vast application in our day to day activities is “Matrices”. A matrix is defined as a collection of numbers or objects that are aligned in rows and columns. The horizontal arrangement of elements is called rows, and the vertical arrangement of elements is called columns. A pair of square brackets enclose the elements in the rows and columns. Its number of rows and columns can determine the dimension of a matrix. For example, if a matrix has an “m” number of rows and an “n” number of columns, then the dimension of a matrix is m × n.

There are different types of matrices, such as square matrix, row matrix, column matrix, diagonal matrix, identity matrix, invertible matrix, transpose matrix, scalar matrix, lower triangular matrix, upper triangular matrix, symmetric matrix, etc. Moreover, matrices have various applications in diverse fields, such as cryptography, computer graphics, physics, geology, economics, mathematics, robotics, signal processing, etc. Now, let us discuss the application of matrices in various fields in detail.

## Physics

Matrix has a wide range of applications in Science, most specifically in Physics. It is used in optics for the reflection and the refraction of light. The matrix plays a major role in calculating battery powers and converting electrical energy into another form of energy. It helps to solve the problems involving Kirchoff’s law of current and voltage. The application of matrix is found in almost all Physics concepts, including quantum mechanics, classical mechanics, optics, etc. which involves the study of physical phenomena, such as the motion of rigid bodies.

## Wireless Communication

The central part of the telecommunication industry is wireless communication. Matrices help to process and represent digital images. It is used to estimate and detect the problems in digital signals. Matrices help in modelling the wireless signals and optimizes them. Thus, the information embedded in the signals can be detected, extracted and processed with the help of matrices.

## Computer Graphics and Cryptography

Matrices play an important role in computer-based applications. For example, matrices can project three-dimensional objects to realistic seeming motions in a two-dimensional screen. Here, the square matrix is used in the linear transformation of objects. Another vital application of matrix in computer-based applications is the encryption of messages. Computer programmers use the matrix and their inverse matrix in the coding of message encryption and decryption. In this process, the audio or video signal is transmitted as a sequence of numbers (i.e.) binary numbers, and it follows the coding theory for solving.

## Geology

In geology, the matrix helps to take seismic surveys. The seismic survey is a geophysical survey that aims to measure the earth’s properties through physical principles, such as gravitational, electric, magnetic theories and so on.. Thus, the matrix helps in the plotting of graphs and helps to do the scientific analysis.

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