What Is a Unitary Matrix?


Quick Answer

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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What Is a Unitary Matrix?
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Full Answer

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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