History and Application of the Matrix

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The word "matrix" is originated from the Latin word "Womb" and the meaning of womb is any place or part that holds envelops, generates something. 

For the first time the matrix was mentioned in ancient China, they called the "magic square". Chinese mathematician Chiu Chang Suan Shu had been used a matrix to solve the linear equations about 200BS. Later some time Arabian known about the magic square and they use it. The idea and applications of arrays/matrices were brought to Europe in 1545 by an Italian mathematician named Gerolamo Cardano.

After the development of the determinant theory in the late 17th century, Gabriel Kramer began developing his theory in the 18^th century and published the Cramer' Rule. The term "matrix" was introduced by James Sylvester in 1850.s and he defined the term matrix is a rectangular array of terms out of which different systems of determinant may be engendered from the womb of a common parent. In 1843, British mathematician Arthur Cayley added Algebra in matrix he defined operations such as addition, subtraction, multiplication, and division of matrices. Jacques Philippe Marie Binet was a French mathematician, physicist, first describe the rule for multiplying matrices in 1812. 

 An English Mathematician named Cullis, is the first man to use the modern bracket notation and had developed this in 1030's. 

$\begin{bmatrix}1 & 2 & 3\\a  & b & c\end{bmatrix}$ or $\begin{pmatrix}1 & 2 & 3\\a  & b & c\end{pmatrix}$

The Mathematician Cullis also demonstrated the first significance notation 

A= [$a_{ij}$]

Use of Matrices Used in Daily Life

            Matrices or matrix is commonly used its mathematics, but have you thought about how important it is or where you can use it? Matrices are using to solve the simple to complex problems of human life. With the help of a matrix, we can represent complex data in a simple and meaningful way. A school can use the matrix to represent the number of students of a different class, number of boys students, and the girls students, number of students passed in different grades in different years. In economics very large matrices are used for the optimization of problems, for example in making the best use of assets, whether labor or capital, in the manufacturing of a product and managing very large supply chains. The matrix is ​​the most useful tool to study the trends of trading stock and the trading model.

            Matrices are applied in the study of electrical circuits, quantum mechanics, and optics. It helps in the calculation of battery power outputs, resistor conversion of electrical energy into another useful energy. Therefore, matrices play a major role in calculations.  Especially in solving the problems using Kirchoff’s laws of voltage and current. It helps in studying quantum physics and in using it. In Geology, matrices are used for making seismic surveys. They are used for plotting graphs, statistics, and to do scientific studies and research in almost different fields. It can help make animations more precise and perfect. In robotics and automation, matrices are the basic components for robot movements. The inputs for controlling robots are obtained based on the calculations from matrices and these are very accurate movements.

References:

F. Livia (2021). Where are matrices are used in daily life? Bitsat https://www.embibe.com/exams/where-are-matrices-used-in-daily-life/
Hamdambek, Q (2019).History and application of the matrix, Tashkent State Technical University, https://www.researchgate.net/publication/340438195_History_and_application_of_the_matrix?
K. Oliver (2009). When was matrix multiplication invented? http://people.math.harvard.edu/~knill/history/matrix/