symmetric operator sentence in Hindi
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- See also Extensions of symmetric operators and unbounded operator.
- This form also makes visible that the skew symmetric operator introduces error when the velocity field diverges.
- Symmetric operators which are not essentially self-adjoint may still have a canonical self-adjoint extension.
- Therefore finding self-adjoint extension for a positive symmetric operator becomes a " matrix completion problem ".
- He contributed also to the classical eigenvalue problem for symmetric operators, introducing the method of orthogonal invariants.
- The compact symmetric operator " G " then has a countable family of eigenvectors which are complete in.
- A symmetric operator has a unique self-adjoint extension if and only if both its deficiency indices are zero.
- He established the spectral theory for bounded symmetric operators in a form very much like that now regarded as standard.
- In the symmetric case, the closedness requirement poses no obstacles, since it is known that all symmetric operators are closable .)
- Such is the case for " non-negative " symmetric operators ( or more generally, operators which are bounded below ).
- In the model, the operator " T " is multiplication by " x " and a densely defined symmetric operator.
- The spectrum of any bounded symmetric operator is real; in particular all its eigenvalues are real, although a symmetric operator may have no eigenvalues.
- The spectrum of any bounded symmetric operator is real; in particular all its eigenvalues are real, although a symmetric operator may have no eigenvalues.
- A densely defined, symmetric operator " T " is essentially self-adjoint if and only if both operators, have dense range.
- According to the reciprocal relations, the damped oscillations in homogeneous closed systems near thermodynamic equilibria are impossible because the spectrum of symmetric operators is real.
- More specifically, finding self-adjoint extensions, with various requirements, of symmetric operators is equivalent to finding unitary extensions of suitable partial isometries.
- A densely defined closed symmetric operator " T " is self-adjoint if and only if " T " " is symmetric.
- As was pointed out in a previous example, a sufficient condition that an unbounded symmetric operator has eigenvectors which form a Hilbert space basis is that it has a compact inverse.
- If the set of eigenvalues for a symmetric operator is non empty, and the eigenvalues are nondegenerate, then it follows from the definition that eigenvectors corresponding to distinct eigenvalues are orthogonal.
- A general version of the spectral theorem which also applies to bounded symmetric operators ( see Reed and Simon, vol . 1, chapter VII, or other books cited ) is stated below.
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