# Tagged Questions

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### Stationary Distribution for Markov-like system?

Let $$A= \begin{pmatrix} 0 & a_{1,2} & a_{1,3} \\ a_{2,1} & 0 & a_{2,3} \\ a_{3,1} & a_{3,2} & 0 \end{pmatrix},$$ B= ...
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### Inverse Transpose of Jacobian Matrix

Let $f:\mathbb{R}^n\mapsto\mathbb{R}^n$ be a bijective function. Fixed $a\in\mathbb{R}^n$. For any $x$ closes to $a$, using Taylor's series we can approximate $f(x)$ by f(x)\approx ...
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### Problem with understanding an equation

I have read the article Short-wavelength Spectral Properties of the Gravity Field from a Range of Regional Data Sets and I don't know how to interpret Equation (10) on page 630, because this equation ...
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### about decomposition of a non-negative definite operators

Hello, Many years before, I had the following problem. We first give a definition. Given a non-negative definite real-valued definite matrix $n^2\times n^2$ matrix $M$, it is called separable if it ...
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### Can always a family of symmetric real matrices depending smoothly on a real parameter be diagonalized by smooth similarity transformations?

This question is related to another question, but it is definitely not the same. Is it always possible to diagonalize (at least locally around each point) a family of symmetric real matrices $A(t)$ ...
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### Question on eigenvalue square root subadditivity

ORIGINAL QUESTION Let $\lambda_{1}\left(\cdot\right)$ be the larger eigenvalue of a $2\times2$ matrix and $\lambda_{2}\left(\cdot\right)$ the smaller eigenvalue of a $2\times2$ matrix. Is it true ...
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### Pinching and positive definite matrices

A pinching over $M_n({\mathbb C})$ is an endomorphism $T$ where the $(i,j)$-entry of $T(M)$ is given either by $0$ or by $m_{ij}$, depending on the pair $(i,j)$. Let us say that a pinching is ...
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### condition number

Hi I have the following matrix A=[a_11 a_12 a_13 1; a_21 a_22 a_23 1; . . . a_n1 a_n2 a_n3 1] I have seen that when some of a_ij are big for instance in the ...
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### An inequality question

Let $M$ be a $3\times2$ matrix. Is it true that for any $x\in\mathbb{R}^{2}$ with $\left\Vert x\right\Vert _{3}=1$ there is some subspace $V$ with dimension $2$ of $\mathbb{R}^{3}$, such that ...