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This is a kind of a follow-up to Question on Hessian of a function (probability question). Suppose I give you a continuous function $ f:\mathbb{R}^n \to \mathbb{R}.$ Is it true that there exists a ($ C^2$ ) function $ g:\mathbb{R}^n \to \mathbb{R},$ such that $ \det(\mbox{Hess}(g)) = f?$ (where $ \mbox{Hess}$ is the Hessian, ofRead more

I have a function $ f:\Re^2\to\Re^2$ and would like to understand why $ |Jf(x)|=\max_\theta|D_\theta f(x)|\cdot\min_\theta|D_\theta f(x)|$ , that is, why the determinant of the Jacobian of $ f$ at $ x$ is equal to the product of min and max of the directional derivatives at $ x$ . I think it must be a moreRead more

I am new to mathematica (less then a month), with the discussion available on this platform and with some tutorial available I have manage to write a code (not a smart one) to solve for the parameter values (values can be real or complex) for which the determinant is zero using Reduce function. Objective: SearchRead more

I have written a code in Haskell that calculates the determinant of a matrix using the laplace expansion. As I have just started learning Haskell, I would like some opinions on how well (structured) the code is written and where I could be able to boost the performance. This is the code: det :: (NumRead more

I am beginner in mathematica. I have the following question: Assume we have a matrix and some of its entries are nonzero and we know which one are. But the nonzero entries can be three different values and we want to calculate the determinant of the matrix for all different cases. How can I doRead more

Finite group $ G=\{x_1,x_2,…x_n\}$ . Consider $ G$ ‘s multiplication table to be an $ n\times n$ matrix $ A$ . Set $ x_i=1$ , $ x_j=0$ ($ j≠i$ ), $ 1≤i≤n$ , then we get $ n$ permutation matrices $ S_i$ ($ 1≤i≤n$ ) s.t. $ A=∑x_iS_i$ . DetA is called groupdet, which isRead more

I carried out the determinant of a 4×4 matrix in two different way: with Laplace and without Laplace (see the attachment please http://s000.tinyupload.com/index.php?file_id=90143443555156237733 ). The Laplace’s rule is applied “manually” in Mathematica (I carried out the 4 determinants of the 4 matrices 3×3; I deleted the second row of the 4×4 matrix). The correct resultRead more

Assume $ A$ is a covariance matrix. You can add further assumption on $ A$ (such as a real symmetric matrix, or nonsingular) in the following calculation. How to find the derivation of $ \det{(A)}$ with respect to the matrix $ A$ ? That is, $ \frac{d}{dA}\det{(A)}=?$ In addicion, $ \frac{d}{dA}(\det{(A)})^{-\frac{1}{2}}=?$Read more