Matrices are first derived from attempting to solve systems of linear equations. These kinds of problems are required to go back towards the most advanced documented examples of mathematical activity. We can do much with matrices besides column or row operations. We can perform addition, subtraction, multiplication, etc., on matrices. We can apply all these operations to examine different mathematical concepts. Many calculators, scientific, electronic spreadsheets, including other computer programs can perform these matrix operations, which is a great help in completing calculations. However, we can understand how these operations are determined and how we can apply these operations in many applications.

Matrices and their operations are useful in different fields which we may or may not observe in detail. For example, matrix multiplication is used widely in the theory of networks, solving a system of linear equations, and the transformation of the coordinate system. Matrices are used in the encryption of messages in the field of computing. Also, these are used to generate three-dimensional graphic images and vivid viewing motion on a two-dimensional computer screen. Some of the crucial uses of matrices in various fields are listed below.

  • Matrices are used to compress electric information and significantly save the information related to fingerprints.
  • We can identify and correct the errors in electronic transmissions with the use of matrices.
  • A message is made as a string of numbers in a binary format for accessible communication, and it supports code theory for solving related issues. Even banks could operate with the transmission of sensitive and secret data. All these activities involve the application of matrices.
  • Matrices are one of the best representation methods for plotting the survey data of everyday things.
  • Matrices describe real-world data regarding special populations, for example, the number of people who have a particular trait. We can also use them to model predictions for the growth of the population.
  • Matrices are also used in many organizations to record the data for various experiments.
  • In the modern wireless connection of the internet over mobile phones, the wireless application protocol also employs matrices in stenography.
  • The science of information security called Cryptography also employs matrices. These types of technologies protect the information in storage or transits.
  • In the page rank algorithms to rank web pages in Google search, Stochastic matrices, including Eigenvector solvers, are helpful.

Thus, we can say that matrices are useful in multiple fields which directly and indirectly help us to solve real world problems. In mathematics, we can define eigen values with the help of matrices and in some cases we can define them even without the application of matrices.

Employing matrices, one can manage a point that is a common mathematical strategy in video game graphics. In graph theory, we can express graphs with the help of matrices. That means it is possible to represent every graph as a matrix. In this case, each column and row of a matrix is the node. Also, the value of the intersection of a row and column element is the strength of the connection between them. Apart from the above, different matrix operations such as translation, rotation and scaling can be used in graphics.