normal operator sentence in Hindi
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- If " X " is a Hilbert space and " T " is a normal operator, then a remarkable result known as the spectral theorem gives an analogue of the diagonalisation theorem for normal finite-dimensional operators ( Hermitian matrices, for example ).
- When the normal operator in question is compact, this version of the spectral theorem reduces to something similar to the finite-dimensional spectral theorem above, except that the operator is expressed as a finite or countably infinite linear combination of projections, that is, the measure consists only of atoms.
- This person can be one of the busiest person during a performance, as the technical master will be needed to do tasks when the normal operator is not there, or when the person that has normally operated certain equipment has left the position for one reason or another, and needs to be replaced.
- To see that this generalises Sz .-Nagy's theorem, note that contraction operators have the unit disc "'D "'as a spectral set, and that normal operators with spectrum in the unit circle " ? " "'D "'are unitary.
- There are however severe difficulties with this particular approach, for example the Hamiltonian operator is not self-adjoint, in fact it is not even a normal operator ( i . e . the operator does not commute with its adjoint ) and so the spectral theorem cannot be used to define the exponential in general.
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