Talk:Pullback
... M to N is bijective, then the pushforward can be defined as $f\_*\; =\; \backslash left\; ...\; it\; for\; more\; reasons\; then\; bijectivity.\; The$pushforward is defined on tangent vectors and contravariant ... vector? 2) can we define a meaningful pushforward of a covector? The answer to both ... the pullback of a vector as the pushforward of the inverse of f. Similarly, we define the pushforward of a covector as the pullback ...
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Talk:Push forward
... that was intended. Never heard it called pushforward though. mat_x 22:10, 2 Mar 2005 ... sheaf theory that are probably pronouced as pushforward or direct image. Charles Matthews 10:38 ... a vector field X on M, the pushforward defines a vector field Y on N ... the same manifold, then the pullback and pushforward define the transformation properties of the covariant ... t push forward, for one thing. The pushforward of a vector field only exists ...
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Pullback
... itself, then the pullback, together with the pushforward, describe the transformation properties of the manifold ... the pullback is in terms of the pushforward of f. Picking a point $p\backslash in\; M$, the pushforward at p is a linear map between ... defined as the matrix transpose of the pushforward; that is, $f^*(p)=\; [f\_*(p\; ...\; has,\; at\; each\; point\; p,\; that\; the$pushforward is the inverse of the pullback, ...
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User:Ashigabou/Matrix calculus
... partial \mathbf{x}}\mathbf{v}. The pushforward or differential of a function f : R ... f_n}{\partial x_m}\\ \end{bmatrix}. The pushforward along f of a vector v in ... transposed; m rows and n columns. The pushforward along F of an n×m matrix Y ...
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User:Charles Matthews/GuilleminSternberg
... Delta section - Pullback of a delta section - Pushforward of a delta section -Current density- Generalized ... Lagrangian submanifold- Pullback of a lagrangian submanifold - Pushforward of a lagrangian submanifold -Lagrangian subspace- Legendre ... set - Pullback of a wave front set - Pushforward of a wave front set -Radon transform ...
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Matrix calculus
... partial \mathbf{x}}\mathbf{v}. The pushforward or differential of a function f : R ... f_n}{\partial x_m}\\ \end{bmatrix}. The pushforward along f of a vector v in ... transposed; m rows and n columns. The pushforward along F of an n×m matrix Y ...
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Lie derivative
... right). where (φ t ) * is the pushforward along the diffeomorphism. In other words, if ... be equivalent using the properties of the pushforward and the Leibniz rule for differentiation. Coordinate ...
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Covariance and contravariance
... the contravariant indices is given by a pushforward. Usage in tensor analysis In tensor analysis ... the contravariant indices is given by a pushforward. See also covariant transformation External links MathWorld ...
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Tangent space
... The derivative of a map Main article: pushforward Every differentiable map f : M → N ... variously the derivative, total derivative, differential, or pushforward of f at p. It is frequently ...
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Cotangent space
... manifolds induces a linear map (called the pushforward or derivative) between the tangent spaces
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