List questions from scalar-fields

Published on 01 Apr 2026 - 10:59

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Differential of scalar product

Published on 13 Apr 2026 - 7:46

355

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If $\vec{\nabla} \times \langle P,Q,Q \rangle=\vec{0}$ iff $Pdx+Qdy+Rdz$ is exact differential form.

Published on 25 Mar 2026 - 1:28

177

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Derivation of $\frac{\partial}{\partial A} \left( y^T A x \right) = y x^T$

Published on 25 Mar 2026 - 1:28

33

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Why is this notation equal to its transpose?

Published on 25 Mar 2026 - 1:32

208

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Gradient of complex scalar field

Published on 25 Mar 2026 - 1:29

463

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Matrix derivative of $Tr(A\log(X))$

Published on 25 Mar 2026 - 1:30

39

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Under what conditions are partial derivatives continuous?

Published on 25 Mar 2026 - 1:25

2.4k

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The conjugate of a scalar is the same scalar in a matrix-scalar multiplication?

Published on 25 Mar 2026 - 1:27

104

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Differentials to derivatives involving trace of matrices

Published on 10 May 2026 - 16:05

2.4k

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Gradient and Hessian of $g(x) = f(Ax + b)$

Published on 25 Mar 2026 - 1:28

970

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How to show the gradient of a composite function $g(z)=f(Az+b)$ is $\nabla g(z)=A^{\top} \nabla f(x)$?

Published on 25 Mar 2026 - 1:29

97

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Computing the gradient of $(X,Y) \mapsto\dfrac{1}{2} \left\lVert A - XY^{T} \right\rVert _{F}^{2}$ via chain rule

Published on 25 Mar 2026 - 1:28

257

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Gradient of $M \mapsto \mbox{tr} \left( A^{-1} M \right) + \mbox{tr} \left( M^{-1} B \right)$

Published on 25 Mar 2026 - 1:28

216

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Gradient of function involving trace of matrix product

Published on 16 Apr 2026 - 7:56

List Question

Gradient of quadratic form

Differential of scalar product

If $\vec{\nabla} \times \langle P,Q,Q \rangle=\vec{0}$ iff $Pdx+Qdy+Rdz$ is exact differential form.

Derivation of $\frac{\partial}{\partial A} \left( y^T A x \right) = y x^T$

Why is this notation equal to its transpose?

Gradient of complex scalar field

Matrix derivative of $Tr(A\log(X))$

Under what conditions are partial derivatives continuous?

The conjugate of a scalar is the same scalar in a matrix-scalar multiplication?

Differentials to derivatives involving trace of matrices

Gradient and Hessian of $g(x) = f(Ax + b)$

How to show the gradient of a composite function $g(z)=f(Az+b)$ is $\nabla g(z)=A^{\top} \nabla f(x)$?

Computing the gradient of $(X,Y) \mapsto\dfrac{1}{2} \left\lVert A - XY^{T} \right\rVert _{F}^{2}$ via chain rule

Gradient of $M \mapsto \mbox{tr} \left( A^{-1} M \right) + \mbox{tr} \left( M^{-1} B \right)$

Gradient of function involving trace of matrix product

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