# Tagged Questions

Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level ...

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### nonnegative solution of nonhomogeneous under-determined linear system of equations

For a set of under-determined linear equations, I was wondering if there is any closed form for all non-negative solutions? Is there a way to analytically characterize the feasibility set of such ...
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### A nice proof that completely bounded (cb) norm of transpose map on $M_n$ is n

In my research of operator algebras and their connection with machine learning I of course use the well know result: For the map $tr:M_n \to M_n$ denoting the transpose map of matrices (meaning ...
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### information measure for matrix that is analogous to rank

Is there a measure for matrix that is analogous to rank of the matrix, but it is continuous on matrix elements? Say, we could say the information in identity matrix $I_n$ is $n$, and when the off-...
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### Matrix norm inequality for C*-Algebras [closed]

Let A a $C^*$-Algebra. I have already shown that the maps $Tr, \sigma: M_n(A)\rightarrow A$ given by $Tr((a_{ij})):=\sum_{i}a_{ii}$ and $\sigma\left(\left(a_{ij}\right)\right)=\sum_{i\text{, }j}a_{ij}$...
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### Determinant of a $4n \times 4n$ block matrix where every block is singular

I have a 4n$\times$4n matrix, which can be written as \begin{pmatrix} 0 & A &B &C \cr D& 0& E & F \cr G& H & 0 & J \cr K& L& M& 0 \end{pmatrix} each ...
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### Matrix transformation [closed]

I want to show that $(I-H^T(-s)H(s))^{-1}$ has no poles on the imaginary axis with $H(s)=C(sI-A)^{-1}B$ and $H^T(-s)=-B^T(sI+A)^{-T}C^T$ is equivalent to $M_\gamma$ has no purely imaginary ...
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### Negative eigenvalue of Toeplitz Hermitian matrix?

I am working on estimation of a covariance matrix and I know that the matrix is Toeplitz. The desired matrix should not produce negative eigenvalues at all. However, sometime my estimation leads to a ...
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### What is the Time Complexity of the Matrix Exponential?

While trying to compute the Matrix Exponential of an $n \times n$ array I decided to take advantage of a Python function called scipy.linalg.expm(). According to ...
Let $A\in M_{n}(\mathbb{C})$ be a Hermitian matrix. If for all $z_1,...,z_n\in\mathbb{C}$, $$\sum_{i,j=1}^{n}A_{ij}z_{i}\overline{z_{j}}\ge 0$$ then A is positive semidefinite. I do not think the ...
Given an explicit polynomial, is there any kind of trick/algorithm to check whether it is a pfaffian of a matrix with linear entries? The pfaffian can be defined as $\sqrt{{\rm det}(A) }$ when $A$ ...