Unitary Matrix Examples

  • Matrix given below is a unitary matrix of order “2 × 2.”

[Tex]A_{2\times2} = \frac{1}{\sqrt{2}}\left[\begin{array}{cc} 1 & 1\\ i & -i \end{array}\right] [/Tex]

  • Matrix given below is a unitary matrix of order “3 × 3.”

[Tex]B_{3\times3} = \left[\begin{array}{ccc} i & 0 & 0\\ 0 & i & 0\\ 0 & 0 & i \end{array}\right] [/Tex]

Unitary Matrix

Unitary Matrix: Unitary Matrices are defined as square matrices of complex numbers such that the product of the conjugate transpose of a unitary matrix, with the unitary matrix itself, gives an identity matrix. Matrices are defined as rectangular arrays in which numbers are arranged in rows and columns. Number of rows and columns determined the size of the matrix. We have different types of matrices, such as rectangular, square, triangular, symmetric, and singular matrices.

In this article, we will learn about a unitary matrix in detail, along with its definition, examples, properties, sample problems etc.

Table of Content

  • What is a Unitary Matrix?
    • Unitary Matrix Definition
  • Unitary Matrix Examples
  • Properties of a Unitary Matrix
  • Solved Examples on Unitary Matrix

Similar Reads

What is a Unitary Matrix?

A square matrix of complex numbers is said to be a unitary matrix if its inverse is equal to the conjugate transpose. In other words, the product of a unitary matrix and its conjugate transpose is equal to the identity matrix. As the determinant of a unitary matrix is not equal to zero, it is a non-singular matrix. The rows and columns of a unitary matrix are orthonormal. If “U” is a unitary matrix and “UH” is its conjugate transpose, then the following condition must be satisfied:...

Unitary Matrix Examples

Matrix given below is a unitary matrix of order “2 × 2.”...

Properties of a Unitary Matrix

Following are some important properties of a unitary matrix:...

Solved Examples on Unitary Matrix

Example 1: Prove that the matrix given below is unitary....

FAQs on Unitary Matrix

Define a matrix....