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covariant
covariant, n. and a. (kəʊˈvɛərɪənt) [f. co- prefix 4 + variant.] A. n. Math. (See quot. 1853.)1853 Sylvester in Phil. Trans. CXLIII. i. 544 Covariant, a function which stands in the same relation to the primitive function from which it is derived as any of its linear transforms do to a similarly der... Oxford English Dictionary
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Covariant is building ChatGPT for robots
6 days ago — Covariant this week announced the launch of RFM-1 (Robotics Foundation Model 1). Peter Chen, the co-founder and CEO of the UC Berkeley ...
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Covariant (invariant theory)
In invariant theory, a branch of algebra, given a group G, a covariant is a G-equivariant polynomial map between linear representations V, W of G. wikipedia.org
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Ted Stinson - Covariant
Experience: Covariant · Location: Menlo Park · 500+ connections on LinkedIn. View Ted Stinson's profile on LinkedIn, a professional community of 1 billion ... www.linkedin.com
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Covariant | Powering the future of automation, today
Address the change and scale of your warehouse operations with robotic automation, built by the world's leading AI research scientists. covariant.ai
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Covariant derivative as a connection on a vector bundle In the Wikipedia article Connexion (vector bundle), such a connection is defined as a function $\Gamma(E) \to \Gamma(E\otimes T^*M)$ . Then the definition of a c...
This is the "classic" covariant derivative in the direction of $X$. is defined by $$D(s_i) = \sum_{\substack{1\le j\le r\\\ 1\le k\le n}} a_{ik}^j s_j\otimes\omega^k \quad\text{for some functions } a_{ik}^j.$$ Then the covariant
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Covariant derivative
To specify the covariant derivative it is enough to specify the covariant derivative of each basis vector field along . By example, the covariant derivatives of vector field . wikipedia.org
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Covariant transformation
The inverse of a covariant transformation is a contravariant transformation. Examples of covariant transformation The derivative of a function transforms covariantly The explicit form of a covariant transformation is best introduced wikipedia.org
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Covariant Derivatives and Swapping Indices Okay,there's a covariant derivative of a rank 2 tensor. Swapping any indices gives a different tensor. Can we associate any physical significance to the swapping? For exampl...
Ok, we have the covariant derivative in the $k$ direction for a rank one tensors, contravariantly $$u^i{}_{;k}=u^i{,k}+\Gamma^i{}_{sk}u^s,$$ and covariantly
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Frobenius covariant
Each covariant is a projection on the eigenspace associated with the eigenvalue . The Frobenius covariant , for i = 1,…, k, is the matrix It is essentially the Lagrange polynomial with matrix argument. wikipedia.org
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Covariant and Directional Covariant Derivative (of Tensors) I'm trying to write precise coordinate and coordinate-free definitions for the covariant and directional covariant derivative of a tensor. I have some workin...
The wording "directional covariant derivative" is not widely used in the literature, but some authors (e.g. Amari, Information Geometry and Its Applications, p. 117) use it, perhaps, to distinguish from the "total covariant derivative" (see e.g.
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Covariant return type
In object-oriented programming, a covariant return type of a method is one that can be replaced by a "narrower" type when the method is overridden in a The relationship between the two covariant return types is usually one which allows substitution of the one type with the other, following the Liskov wikipedia.org
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Connections and covariant derivatives Let $A$ be a connection on a principal $G$-bundle $P$, let $\chi :G\rightarrow GL(V)$ be a representation of $G$, and let $E:=P\times _\chi V$ be the associated gauge bundle. Then...
Let $d_A$ denote the covariant derivative on $P$ induced by $A$. Then the induced covariant derivative $\nabla^A$ on $P \times_\chi V$ induced by $A$ and $\chi$ is the map making the following diagram commute: $$\require
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Second covariant derivative
In the math branches of differential geometry and vector calculus, the second covariant derivative, or the second order covariant derivative, of a vector Then the second covariant derivative can be defined as the composition of the two ∇s as follows: For example, given vector fields u, v, w, a second covariant wikipedia.org
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Express covariant derivative in terms of exterior derivative I know there is an intimate relation between covariant, Lie and exterior derivative. I know that the covariant derivative requires more structure than the e...
As it is well known, the Levi-Civita connection can be implicitly defined via the Koszul formula. P.Petersen in his "Riemannian Geometry" gives a nice presentation of this formula: $$ 2 g (\nabla_Y X, Z) = (L_X g) (Y, Z) + (d \theta_X) (Y, Z) $$ where $g$ is a Riemannian metric, $X, Y, Z$ are some v...
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