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IEVref: | 102-06-28 | ID: | |

Language: | en | Status: Standard | |

Term: | unitary matrix | ||

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Definition: | regular square matrix with complex elements for which the inverse AA^{−1} is equal to the Hermitian conjugate matrix A^{H}Note 1 to entry: For a unitary matrix with elements $\sum _{i}{A}_{ij}{A}_{ik}^{*}}={\delta}_{jk$ and $\sum _{k}{A}_{ik}{A}_{jk}^{*}}={\delta}_{ij$ where ${\delta}_{jk}$ and ${\delta}_{ij}$ are Kronecker deltas. Note 2 to entry: Any orthogonal matrix with real elements is a unitary matrix. | ||

Publication date: | 2008-08 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO 2017-08-25: Corrected order of I and sub tags. LMO | ||

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Note 1 to entry: For a unitary matrix with elements *A _{ij}*:

$\sum _{i}{A}_{ij}{A}_{ik}^{*}}={\delta}_{jk$ and $\sum _{k}{A}_{ik}{A}_{jk}^{*}}={\delta}_{ij$

where ${\delta}_{jk}$ and ${\delta}_{ij}$ are Kronecker deltas.

Note 2 to entry: Any orthogonal matrix with real elements is a unitary matrix.