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  2. Special linear group - Wikipedia

    en.wikipedia.org/wiki/Special_linear_group

    In mathematics, the special linear group SL(n, R) of degree n over a commutative ring R is the set of n × n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant

  3. SL2 (R) - Wikipedia

    en.wikipedia.org/wiki/SL2(R)

    SL(2, R) is the group of all linear transformations of R 2 that preserve oriented area. It is isomorphic to the symplectic group Sp(2, R) and the special unitary group SU(1, 1). It is also isomorphic to the group of unit-length coquaternions. The group SL ± (2, R) preserves unoriented area: it may reverse orientation.

  4. Projective linear group - Wikipedia

    en.wikipedia.org/wiki/Projective_linear_group

    The projective special linear group, PSL, is defined analogously, as the induced action of the special linear group on the associated projective space. Explicitly: PSL(V) = SL(V) / SZ(V) where SL(V) is the special linear group over V and SZ(V) is the subgroup of scalar transformations with unit determinant.

  5. Synchronous impedance curve - Wikipedia

    en.wikipedia.org/wiki/Synchronous_impedance_curve

    The name "synchronous impedance curve" is due to the fact that in the short-circuit condition all the generated voltage dissipates across the generator internal synchronous impedance . [ 2 ] The curve is obtained by rotating the generator at the rated RPM with the output terminals shorted and the output current going to 100% of the rated for ...

  6. Special linear Lie algebra - Wikipedia

    en.wikipedia.org/wiki/Special_linear_Lie_algebra

    In mathematics, the special linear Lie algebra of order over a field, denoted or (,), is the Lie algebra of all the matrices (with entries in ) with trace zero and with the Lie bracket [,]:= given by the commutator. This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras.

  7. PSL (2,7) - Wikipedia

    en.wikipedia.org/wiki/PSL(2,7)

    PSL(2, 2) is isomorphic to the symmetric group S 3, and PSL(2, 3) is isomorphic to alternating group A 4. In fact, PSL(2, 7) is the second smallest nonabelian simple group, after the alternating group A 5 = PSL(2, 5) = PSL(2, 4). The number of conjugacy classes and irreducible representations is 6. The sizes of conjugacy classes are 1, 21, 42 ...

  8. Generator (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Generator_(mathematics)

    The generator of any continuous symmetry implied by Noether's theorem, the generators of a Lie group being a special case. In this case, a generator is sometimes called a charge or Noether charge, examples include: angular momentum as the generator of rotations, [3] linear momentum as the generator of translations, [3]

  9. Switched reluctance linear motor - Wikipedia

    en.wikipedia.org/wiki/Switched_reluctance_linear...

    Then a linear stepper motor of the variable reluctance type was for serial printer applications. In 1977 J.W. Finch researcher on the Linear Vernier Reluctance Stepper Motor to replace a mechanical conveyor for a trolley. In 1988-89, Takamaya developed a linear motor based on the principle of variable reluctance.