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