Q:

# What is a unitary matrix?

A:

A unitary matrix is a matrix that when multiplied by its complex conjugate transpose matrix, equals the identity matrix. This implies that the complex conjugate transpose of a matrix is equal to the inverse of the unitary matrix. Unitary matrices have several applications in different fields of science and engineering, such as quantum mechanics.

## Keep Learning

Credit: Tetra Images N/A Getty Images

Unitary matrices with entries that are all real are orthogonal matrices. The rows of unitary matrices are a unitary basis. This means that each row has length one and their Hermitian inner product equals zero. Various linear algebra techniques can be used to determine if a matrix is unitary.

Sources:

## Related Questions

• A: The inverse of a two-by-two matrix is another two-by-two matrix that, when multiplied by the original matrix, gives the identity matrix. Gauss-Jordan elimi... Full Answer >
Filed Under:
• A: The inverse of a 2x2 matrix is the matrix that results in the identity matrix when multiplied by the first matrix. The values for the inverse of a 2x2 matr... Full Answer >
Filed Under:
• A: To rationalize an imaginary denominator, multiply both the numerator and denominator by the complex conjugate of the denominator. Multiply out the terms in... Full Answer >
Filed Under:
• A: A 3x3 matrix is a matrix that consists of three rows and three columns. Matrices are an array of numbers that can be added, subtracted and multiplied.... Full Answer >
Filed Under:
PEOPLE SEARCH FOR