Eigenvectors and eigenvalues are two fundamental concepts in linear algebra that are widely used in various fields such as physics, engineering, and computer science. Though the terms might sound technical and difficult, they have practical applications in a wide range of areas.
In this article, I will give a short explanation of the concept of eigenvectors and eigenvalues, and give some examples of their real-world applications.
What are Eigenvectors and Eigenvalues?
In simple terms, an eigenvector is a special vector that remains in the same direction when a linear transformation is applied to it, but it may change in magnitude.
An eigenvalue is a scalar value that represents how much the eigenvector gets scaled during the transformation.
One way to think about eigenvectors and eigenvalues is to consider a spinning top. The axis of rotation of the top is an eigenvector, as it remains in the same direction even when the top spins. The eigenvalue in this case represents the speed at which the top is spinning.
