This has the geometric interpretation that multiplication by a unit complex number is a proper rotation in the complex plane, and every such rotation is of this form.
22.
As the symbol " ? ijk " is a pseudotensor, pseudovector operators are invariant up to a sign : + 1 for proper rotations and " 1 for improper rotations.
23.
In either the narrower or the wider senses, the composition of two improper rotations is a proper rotation, and the composition of an improper and a proper rotation is an improper rotation.
24.
In either the narrower or the wider senses, the composition of two improper rotations is a proper rotation, and the composition of an improper and a proper rotation is an improper rotation.
25.
The orthogonal-by-matrices with determinant form a normal subgroup of known as the "'special orthogonal group "', consisting of all proper rotations . ( More precisely, is the Dickson invariant, discussed below . ).
26.
Clearly, G 1 is isomorphic to C12, the group of proper rotations of a regular dodecagon . \ zeta = 8 + j6 is a group generator corresponding to a counter-clockwise rotation of 2? / 12 = 30?
27.
It is this line that allows an improper rotation to be decomposed into a proper rotation about the line followed by a reflection that flips the line over ( i . e ., in a plane perpendicular to the line ).
28.
In fact, all proper rotation 3? rotation matrices form a group, usually denoted by SO ( 3 ) ( the special orthogonal group in 3 dimensions ) and all matrices with the same trace form an equivalence class in this group.
29.
Mikasa Sports, manufacturer of the new colored ball, claims that the new ball benefits teams by making it easier for them to keep track of their balls, differentiating the women s balls from the men s and teaching proper rotation on the ball.
30.
Rocker arm rollers can be inspected for proper rotation, potential valvetrain problems such as insufficient or excessive clearance can be observed, piston ring movement in the ring grooves indicating excessive groove wear can be observed, broken valvesprings can be more easily seen, and so on.
