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# What Is a Unitary Matrix?

**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.

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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.

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Q:
## What Is the Inverse of a 2x2 Matrix?

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: -
Q:
## What Is the Inverse of 2x2 Matrix?

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: -
Q:
## How Are Imaginary Denominators Rationalized?

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: -
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## How Do You Determine How Many Entries Are in a Matrix?

A: To determine the number of entries in a matrix, count the number of elements inside the brackets. For example, a matrix having the elements -5, 2, 10, 4, 1... Full Answer >Filed Under: