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What is the link between contraction mappings and the eigenvalues of their Jacobian?

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#calculus #real-analysis #eigenvalues-eigenvectors #jacobian
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Jacobian matrix negative sign when transforming variables for integrating over plane?

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#transformation #surface-integrals #jacobian
144
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Gradient of angle between triangles in terms of field over vertices

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#geometry #triangles #gradient-descent #jacobian
2.5k
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Jacobian of three functions

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#calculus #jacobian
404
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Isometric deformation implies $ J^TJ=I$

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#isometry #jacobian
46
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How to express the integrands of lengths, areas, (hyper)volumes in a general way?

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#matrices #determinant #closed-form #jacobian
386
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Is the Jacobian a divergence of some vector field? (manifolds)

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#riemannian-geometry #calculus-of-variations #divergence-operator #jacobian
2.2k
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An explanation for undergraduated students about why the Jacobian conjecture is hard

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#abstract-algebra #multivariable-calculus #intuition #conjectures #jacobian
105
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Apache Math Commons: non-linear optimization

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#optimization #partial-derivative #jacobian
430
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How to define the k-dimensional Lebesgue measure $\lambda^{k,n}$ on $R^n$ when $k<n$

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#measure-theory #reference-request #lebesgue-integral #lebesgue-measure #jacobian
109
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Double integral using jacobian

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#jacobian
44
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Is $F:\mathbb{R}^m \to \mathbb{R}^n$ invertible?

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#inverse-function #jacobian
169
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Double integration using Jacobians

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#multivariable-calculus #jacobian
13.5k
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Jacobian of implicit functions

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#multivariable-calculus #jacobian #implicit-function
391
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Determinant of a 3x3 matrix vanishes?

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#matrices #determinant #jacobian

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