How is Linear Algebra used in Physics?

"Why is Linear Algebra taught?" , "What good it does to physics students?", "How is linear algebra used in physics?" are some of the questions I asked myself when I had to learn linear algebra in my physics course.

I was not able to understand why this box of numbers (matrices) and vectors is of any relevance to physics. But as I progressed in my course and realized that those were not just box of numbers but magical box of numbers that can solve complex problems in physics.

Linear algebra deals with vectors and matrices, which are nothing but a group of numbers but can do quite a bit of lot of things. Anything that solves problems is of great importance in physics. Because physics is all about solving problems and understanding the world around us.

In this article, we will discuss how linear algebra is used in physics and what are the applications of linear algebra in physics.

Applications of Linear Algebra in Physics

To Understand the concept of space beyond the basics of geometry requires Linear Algebra.

Things like Eigen Vectors, Eigen values, Principal Axis, rotations, relativity, etc are all based on Linear Algebra.

Motion and Forces

In Physics, vectors are used to represent motion and forces in universe. Because vector is a mathematical entity with magnitude and direction. And so do the motion and forces in physics.

Vectors in Motion

Different properties of moving objects like speed, velocity, direction is represented using vectors. Even the acceleration of the object is represented using vectors (rate of change of velocity).

Vectors in Forces

Force can be represented as a vector itself. A force applied has both magnitude and direction.

As you can see, linear algebra components like vectors and matrices are used to represent motion and forces in physics. We have been using linear algebra in physics without even realizing it.

Electricity and Magnetism

In circuit Analysis, Linear algebra helps to set up equations and solve them using matrices. Matrices are used to figure out current, voltage, and power in different parts of circuit.

Scientists create a mathematical model of electro magnetic fields using vectors and matrices. These model helps to predict how magnet will behave or how electric charges will interact with each other.

Before testing in real life, they test their model using linear algebra to make smart guesses.

Optics and Length

It may be a bit of a suprise but scientists use linear algebra to calculate the strength of a light beam. Its represented by a vector.

Scientists also use linear algebra to build better lenses, mirrors and clear cameras. The length of the mirror or lens is represented by a vector.

Temperature Distribution

Linear algebra is used to measure temperature distribution. I have not studied this in detail, but I know it involves solving a system of linear equations.

Vector is used to represent the transfer and strength of warmth as it moves from one point to another.

Watch This Video to Learn about how linear algebra is used in temperature distribution.

Some other application of linear algebra in physics are:


The motivation behind this post was anon user in MathEducator StackExchange.

He says explaining students how physics is related to linear algebra can help appreciate students learning mathematics appreciate the phyics course and students learning physics learn and understand the underlying concept of linear algebra

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