| 41. | Mathematically, A is a self-adjoint operator on a Hilbert space.
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| 42. | By the spectral theorem for self-adjoint operators,
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| 43. | A particular case of this happens when a continuous functor admits a left adjoint.
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| 44. | In fact it is the adjoint representation of.
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| 45. | More generally, any type of limit is right adjoint to a diagonal functor.
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| 46. | Taking the conjugate transpose ( or adjoint ) of complex matrices generalizes complex conjugation.
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| 47. | Keep in mind that " adjunct " is not adjugate or adjoint.
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| 48. | A Lie algebra is said to be reductive if the adjoint representation is semisimple.
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| 49. | This use of language strongly suggests that we are dealing here with adjoint functors.
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| 50. | In its adjoint representation is hyperbolic, i . e . has real eigenvalues.
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