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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
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.
The subgroup fixing one of the 759 (= 3·11·23) octads of the Golay code or Steiner system is the octad group 2 4:A 8, order 322560, with orbits of size 8 and 16. The linear group GL(4,2) has an exceptional isomorphism to the alternating group A 8.
Also well known are the Norton and Thévenin equivalent current generator and voltage generator circuits respectively, as is the Y-Δ transform. None of these are discussed in detail here; the individual linked articles should be consulted. The number of equivalent circuits that a linear network can be transformed into is unbounded.
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 ...
Current mode logic (CML), or source-coupled logic (SCL), is a digital design style used both for logic gates and for board-level digital signaling of digital data.. The basic principle of CML is that current from a constant current generator is steered between two alternate paths depending on whether a logic zero or logic one is being represented.
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]
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.