MATRICES – THE MATRIX IS EVERYWHERE

Introduction

The era we are going to talk about this time is after the 1800s closer to the modern era where different inventions like complex plain, matrices, group theory, Poisson distribution, Venn diagram, topology, etc. were finding a thing which were visible and noticed in the world of math earlier too. In the world of mathematics, the matrices were just introduced and some methods to solve were given in late eras but this era brought the concept into consideration.

Meaning of matrices

Matrices are rectangular grids of elements that are arranged in rows and columns with square brackets and enclosed in them. These rows and columns are possible to expand indefinitely, which makes it possible for the matrices to store vast amounts of data in an elegant and compact form. Although in a matrix, there are several elements that are going to be treated like one unit. Matrices have applications in mathematics, physics, and computer science, such as in computer graphics and describing the flow of a fluid.

Sums and subtractions

The dimensions of a matrix are really important, as operations such as addition and subtraction require the matrices involved to have the same dimensions. The 2 × 2 matrices below are square matrices, meaning that they have the same number of rows as they have columns. In the two matrices with the same dimensions, the number with the same row and column gets added and subtracted from each other.      

Multiplication of matrices

Matrix multiplication is, however, quite different from the multiplication of numbers. Not all matrices can be multiplied together; in matrix multiplication, AB can only be calculated if the row count of B is the same as the column count of A. Matrix multiplication is non-commutative, meaning that even where both A and B are square matrices, AB is not equal to BA. The example is given in the following image

Multiplying two matrices together is achieved by multiplying the horizontal numbers in the first matrix by the vertical numbers in the second and adding the following obtained result. Switching around the order in which the two matrices are multiplied produces a different result as shown here with the multiplication of two square matrices.

Conclusion

The matrices when came into notice were unable to discover the route how to getting universally accepted but the formulations and required uses of these helped them grow. The concepts of matrices like their additions, subtraction, multiplication, and division were unique to the world of mathematics and this uniqueness was the key to unlocking the doors of the mathematical world. The era of 1800-1900 is bringing up those concepts which were in use before but their acceptance was missing. Now this concept is known to every college student and getting some new things about this makes it more interesting to learn.