| Hermitian Adjoint |
Article Index for Hermitian |
Information AboutHermitian Adjoint |
| CATEGORIES ABOUT HERMITIAN ADJOINT | |
| operator theory | |
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Adjoints of operators generalize Conjugate Transpose s of square matrices to (possibly) infinite-dimensional situations. If one thinks of operators on a Hilbert space as "generalized complex numbers", then the adjoint of an operator plays the role of the Complex Conjugate of a complex number.
DEFINITION FOR BOUNDED OPERATORS Suppose ''H'' is a ). Using the Riesz Representation Theorem , one can show that there exists a unique continuous linear operator
PROPERTIES Immediate properties:
If we define the Operator Norm of ''A'' by | ||
| :<math> \ A^ \ {op} | \ A \ _{op} </math> |
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| :<math> \ A^ A \ {op} | \ A \ _{op}^2 </math> |
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