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- Rotational_invariance abstract "In mathematics, a function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations are applied to its argument. For example, the function f(x,y) = x2 + y2 is invariant under rotations of the plane around the origin.For a function from a space X to itself, or for an operator that acts on such functions, rotational invariance may also mean that the function or operator commutes with rotations of X. An example is the two-dimensional Laplace operator Δ f = ∂xx f + ∂yy f: if g is the function g(p) = f(r(p)), where r is any rotation, then (Δ g)(p) = (Δ f)(r(p)); that is, rotating a function merely rotates its Laplacian. In physics, if a system behaves the same regardless of how it is oriented in space, then its Lagrangian is rotationally invariant. According to Noether's theorem, if the action (the integral over time of its Lagrangian) of a physical system is invariant under rotation, then angular momentum is conserved.".
- Rotational_invariance wikiPageID "424202".
- Rotational_invariance wikiPageRevisionID "543746079".
- Rotational_invariance hasPhotoCollection Rotational_invariance.
- Rotational_invariance subject Category:Conservation_laws.
- Rotational_invariance subject Category:Rotational_symmetry.
- Rotational_invariance type Abstraction100002137.
- Rotational_invariance type Collection107951464.
- Rotational_invariance type ConservationLaws.
- Rotational_invariance type Group100031264.
- Rotational_invariance type Law108441203.
- Rotational_invariance comment "In mathematics, a function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations are applied to its argument. For example, the function f(x,y) = x2 + y2 is invariant under rotations of the plane around the origin.For a function from a space X to itself, or for an operator that acts on such functions, rotational invariance may also mean that the function or operator commutes with rotations of X.".
- Rotational_invariance label "Rotational invariance".
- Rotational_invariance label "旋轉不變性".
- Rotational_invariance sameAs m.026tst.
- Rotational_invariance sameAs Q388829.
- Rotational_invariance sameAs Q388829.
- Rotational_invariance sameAs Rotational_invariance.
- Rotational_invariance wasDerivedFrom Rotational_invariance?oldid=543746079.
- Rotational_invariance isPrimaryTopicOf Rotational_invariance.