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topic:math:linalg:operator
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| topic:math:linalg:operator [2023/02/13 19:00] – samuel | topic:math:linalg:operator [2023/02/14 17:14] (current) – [Operator (Matrix) properties] samuel | ||
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| ===== Operator (Matrix) properties ===== | ===== Operator (Matrix) properties ===== | ||
| - | * U^\dagger is the adjoint of $U$, and in matrix representation is given by $(U^*)^T$, where $^*$ marks the complex conjugate and $^T$ the transpose. | + | * $U^\dagger$ is the adjoint of $U$, and in matrix representation is given by $(U^*)^T$, where $^*$ marks the complex conjugate and $^T$ the transpose. |
| * An operator (matrix) $U$ is said to be normal if $U^\dagger U = U U^\dagger$. | * An operator (matrix) $U$ is said to be normal if $U^\dagger U = U U^\dagger$. | ||
| * A normal operator is diagonizable (spectral decomposition) | * A normal operator is diagonizable (spectral decomposition) | ||
| Line 14: | Line 14: | ||
| * An operator (matrix) | * An operator (matrix) | ||
| * A hermitian operator is normal. | * A hermitian operator is normal. | ||
| - | * | ||
topic/math/linalg/operator.1676314837.txt.gz · Last modified: by samuel
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