What is Linear Algebra?

What is Linear Algebra?

Linear algebra is an integral part of Mathematics that deals with vectors. Have you ever wondered why Linear algebra is called” Linear”?? That is because the equations used are in a straight line in the Cartesian plane. Linear algebra uses letters and symbols, which are called variables.

The study is focused on analyzing the quantities with direction and magnitude. Linear algebra deals with linear equations such as linear maps. The linear maps are represented in vector spaces and through metrics. Linear algebra is simplified into three categories: linear equations, Vectors and matrices.

Why Linear Algebra is essential

Linear algebra is an essential part of mathematics as it is considered a fundamental concept in geometry, machine learning and functional analysis, physics, economics, and, at times, medicine. Linear algebra is a mathematical tool that helps to solve every real-world problem. Linear algebra has its application in every sphere of life, from psychology to engineering. It allows models to be modelled and computed, leading to a wide application of this incredible mathematical tool.

Application of Linear Algebra

Data science: Linear algebra has wide application in data science for data manipulation. Linear algebra can be used in:

Machine learning: Linear algebra is used to build models in machine learning. Linear algebra can represent data as arrays, matrices and vectors. Linear algebra can perform transformations and optimizations to find solutions on large data sets. Data classification and error removal from trained data are possible with Linear algebra in machine learning. You can understand algorithms if you know linear algebra and can make better decisions.

Network Analysis: Linear algebra can optimize social networks, internet traffic, and logistical networks and analyze them with the shortest path. It can solve optimization problems by finding the shortest route.

Computer science: Linear algebra enables numerical computing. It can break down the non-linear problems into smaller linear subproblems. You can have a better understanding of algorithms with Linear algebra. You can use linear algebra in 2D graphics, graph algorithms, computer vision, computational biology, web search, quantum computation etc.

Economics: Linear algebra helps model economic aggregates in economics, especially macroeconomics. In microeconomics, linear algebra helps to study market equilibrium. It also helps create powerful tools for modelling and analyzing financial systems. Even if you aspire to pursue a bachelor’s in economics, you will study economics, statistics, and linear algebra.

Statistics: Linear algebra helps in data organization and to solve equations in statistics. It can simplify complex problems with appropriate solutions.

Biology: Linear algebra is useful in computing population biology, genetics, and analysis of ecosystems.

Health care: Linear algebra is useful in disease progression medical imaging, to study the genetics and many more.

Medicine: Linear algebra is useful in medical devices like CT scanners, ultrasound, and MRIs.

Who should know Linear Algebra?

Linear algebra is an influential mathematical means that can be used to do wonders in several industries. Linear algebra should be studied by a high school student, a 12th standard student who has opted for Math. Physics and chemistry, an economist, lab technicians who operate on medical devices, biotechnology professionals, statisticians, economists, physicists, biologists, genetics professionals, health care professionals, data scientists, machine learning & NLP professionals, etc, should know linear algebra.

Conclusion

Linear algebra has a wide application in solving real-world problems. The subject is introduced to students at the school level. Unfortunately, students neglect the subject and don’t pay attention to gaining knowledge. It's never too late to learn anything, and so is Linear algebra.

We teach linear algebra in a manner you find interesting and lay your foundation for a prospecting career in whichever career option you choose.