How to implement the concept of matrices in real life Advice, Complex Maths Guide

How to implement the concept of matrices in real life?

Nov 17, 2020

Matrix mathematics is a tricky concept. Due to the complexity of the operations in matrix mathematics, it gives nightmares to many. Most mathematical concepts are broadly visualizable, but matrix mathematics at a high level can be beyond visualization. They can span into multiple dimensions – sometimes more than 3 – and carrying out basic operations on matrices is more difficult than on any other type of numerical element. Matrix multiplication, in particular, is a long and arduous task, and matrices are operated using code than on paper.

The reason that matrices are taught compulsorily at all levels of education, despite being such a difficult concept, is that they have tons of uses in real life. Matrices are used in various walks of life, and their uses are only growing by the day. Almost every piece of code you see in the smallest of technology  uses matrices in one way or another. Here, welay before you some of the many uses of matrices in our day to day lives.

  • Encryption

There are various examples of encryption that you will be able to find in your daily life. Almost all the messages that you send on instant messaging applications are end to end encrypted. If you use an iPhone, all the information that you store on it is encrypted. The emails that you send using most email accounts are made to go through some form of encryption. In fact, encryption is the go-to method to ensure security  in a way that most others can’t. Encryption is done using code, which is then deployed in applications.

Matrices are used heavily in the field of encryption. The greater the level of encryption is, the larger will be the matrices used in creating that. The key that allows the user to encode data and then later decode it is formed entirely of matrices. Matrices can also be used to store the data that has been encrypted. Matrices with multiple dimensions will generally help ensure that the security of the encrypted data is better. The scrambling of data for encryption is done using matrices, and later matrix operations help users decode the data and retrieve it in its original form.

Video Games

The video game industry has been booming beyond proportion in the past few years. Not only the number of video game players increased lately, the quality of video games in the market has also improved tremendously. The graphics in video games are  becoming more realistic. The gameplay of these games has become immensely complex, and the data generated by them has increased in size by the year with the new versions of video games launching every now and then. Driven by the demand of millions of gamers around the world, the three-dimensional graphics of video games have also  improved with every new version, along with  the world in which the games are premised.

This improvement in three-dimensional graphics is driven immensely by the concept of matrices. Since video games are made in either two or three dimensions, the positions of particular elements are governed by Cartesian Coordinates. Since matrices are a convenient method of expressing Cartesian Coordinates, they are mostly used for this purpose. As the graphics improves, the number of these coordinates also increases. This increases the size of the matrix correspondingly, thus following the rule of increased complexity with increased matrix size.

Business

The world of business runs on strategy, tact and speculation. Speculation is hard, and a lot of firms often rely on data to help plan their next steps. This has given rise to forecasting as a basic requirement  of businesses, in which future trends of various quantities are tried to be forecast using data from past transactions, other market transactions, and business climate. Using these factors and assigning them weights allow business analysts to develop a complete forecasting model which can help you determine where your next investment should be made. Large value investors will generally use a significant amount of data to decide where to put large swathes of money.

The financial models extensively use the concept of matrices. Most of the data that are  used in these data science models are  stored in the form of matrices, and later, scores of matrix operations are performed on them. Furthermore, the resultant of the models are also generally in the form of a matrix, out of which certain elements are reported as the final result after analysis. Business leaders generally promote the setting up of better infrastructure to store such data that might help them in carrying out large sum transactions.

Civil Works

Buildings, bridges and roads are all around us.  Buildings require complex concepts of engineering, knowledge of materials and architectural capabilities. However, any kind of building or tower is not just a  structure that is visible outside. It needs to have  a foundation that can sustain its weight. It must be built in such a way that it can withstand adverse climate. It must pass safety regulations, and sustain the weight of those who will be using it once it is complete. All these considerations call for important concepts in solid mechanics and architecture.

These concepts are realizable only through matrices. The various inherent properties of materials are entered into matrices before they are analyzed. The strength and rigidity of any structure can be simulated using physics on the computer by using matrices. A number of structural analysis software are now available as open-source, which allow users of all levels to calculate the impact that various kinds of force on any structure that is going to be built. These software have taken a central place in the analysis of any prospective civil works in modern times.

Robotics

A couple of decades ago, robotics was touted as the next big thing in technology. Now, it is all around us. While the popular focus has always been on humanoid robots, the real application of robots has been in industrial manufacturing and retail, where they have led to significant automation. Robots are more than just the metal structure they are usually envisioned. They need to know what to do – the reason that they are going to be used. This is taught to them through code.

The subject of robotics is a part of computer-aided manufacturing. Each of the coordinates that a robot needs to know are fed to it using codes. Codes make extensive use of matrices to explain tasks, as well as how to do the task. As with most computer applications involving Cartesian Coordinates, in robotics too, these coordinates take the form of matrices on which matrix operations are carried out to modify them.

Recommendation Engines

Machine learning is a major buzzword of this era. While scores of people consider it a concept beyond reach, not many realized how pervasive it is all over the internet. Recommendation engines of websites use machine learning to recommend videos, posts and articles that they think you would like, based on your web or browser history. The advertisements you see on multiple websites also use machine learning. Not everybody sees the same ads on the same website, the ads you see are based on your browsing history and what the website or advertisement provides calculates that you are most likely to click on.

This calculation is done using matrices. The concept of machine learning is built almost entirely on matrices. Sets of data are entered in matrix form, and an algorithm allows the engine to learn the data entered and predict future likelihoods depending on its learning.

Conclusion

Matrices are  very tricky concepts, but are also equally useful. They are used in many fields from the internet to construction, and from robotics to business predictions. They are also used in several mathematical games and can help you get better at math with Cuemath Games. These advantages and uses of matrices make them an essential concept to learn for any student interested in mathematics and its uses in the everyday lives of all people.

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