An Introduction To Eigenvectors & Eigenvalues Towards Quantum Computing

Learn the mathematical basis of quantum measurements by performing them by hand.

Photograph of David Hilbert, an incredible mathematician who laid the theoretical groundwork for understanding eigenvalues and eigenvectors within quantum systems and the development of Hilbert space that provides the bedrock for quantum mechanics. (Source: Wikimedia Commons)

Eigenvectors & Eigenvalues are two important terms you will encounter multiple times when reading about Quantum Computing.

These terms are crucial to understand, and this lesson is all about them.

Let’s do this step by step.

Matrices

We start with Matrices that we have extensively discussed in a previous lesson.

A Matrix is a rectangular array of numbers (elements).

A m x n matrix has m rows and n columns.

For example, a 3 x 2 matrix is shown below:

Matrices are used to describe linear transformations between vectors.

Multiplying a matrix by a vector is equivalent to applying the linear transformation represented by that matrix to the vector.

Square Matrix

A matrix with the same number of rows and columns is called a Square matrix.