Use cotangent in a sentence - Example Sentences for cotangent
According to the Major League Baseball system, a high fly will descend at an angle whose cotangent is 0.
where ? is the holomorphic cotangent bundle and the notation ?2 means the 'tensor square' ('not' the second exterior power).
The cotangent bundle 'X'='T'*'M', since it is a vector bundle, can be regarded as a manifold in its own right.
All cotangent spaces on a manifold have the same dimension of a vector space, equal to the dimension of the manifold.
'Cotangent bundle', the vector bundle of cotangent spaces on a manifold.
The tangent space and the cotangent space at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms.
Proving this form is, indeed, symplectic can be done by noting that being symplectic is a local property: since the cotangent bundle is locally trivial, this definition need only be checked on \mathbb^n \times \mathbb^n.
Smooth function Fiber bundle of the cotangent bundle are differential one-forms.
Alternatively, if 'X' is a real vector space and 'Y' is its dual space, then for each point 'x' of 'X' and 'y' of 'Y', there is a natural identification of the cotangent spaces T*'X'x' with 'Y' and T*'Y'y' with 'X'.
It is the natural way to view the range of the tangent and cotangent functions of trigonometry: tan('x') approaches the single point at infinity as 'x' approaches either \scriptstyle+\pi/2 or \scriptstyle-\pi/2 from either direction.
"Suppose that '?':'M'› 'N' is a smooth map between smooth manifolds 'M' and 'N'; then there is an associated linear map from the space of 1-forms on 'N' (the linear space of section (fiber bundle) of the cotangent bundle) to the space of 1-forms on 'M'."
This yields the correspondence between the tangent space defined via derivations and the tangent space defined via the cotangent space.
The cotangent space will then consist of all the possible first-order behaviors of a function near x.
"where the ξ'i' are the fiber coordinates on the cotangent bundle induced by the coordinate differentials d'x'i'."
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The word cotangent
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