# Tagged Questions

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### Matrices with functions as entries

I am interested is studying matrices which have functional entries. Specifically I am looking at quadratic forms of the type $x^T Q(x) x$ where $Q(x)$ is a matrix whose entries are functions of $x$. I ...
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### Quadratic form between a full row rank matrix and a positive definite matrix

Let $A\in\mathbb{R}^{n\times n}$ be a positive definite matrix and $B\in\mathbb{R}^{m\times n}$ (with $n>m$) is a full rank matrix ($\text{rank}B=m$). Could you please give me a reference for ...
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### How to test if $m$ vectors are linearly dependent when they are $n$ dimensional and $m < n$

I'll be shocked if this isn't a duplicate, but I haven't had a lot of luck finding an answer to this so far. How do you test if a set of vectors $v_1, \ldots v_m \in \mathbb{R}^n$ are linearly ...
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### Birkhoff-Neumann like result for stochastic matrices?

during my research I came along a nice lemma which looks like a Birkhoff-Neumann-theorem result, but in a version for stochastic matrices. Namely, I have: Lemma. Let $M$ be a stochastic matrix, then ...
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### Matrix inequality, now what?

I am looking for some motivations. I am reading a book about matrix inequality. e.g. Courant–Fischer equality, eigenvalue of sum of two matrix, ... My question is, so what kind of problems I should ...
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### Largest average principal submatrix of a symmetric matrix.

I am wondering if there exists literature on the following problem: Let $X$ be an $n \times n$ symmetric matrix. How do you identify the $k \times k$ principal submatrix of $X$ with the largest ...
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### Regular matrices references

Can someone suggest me a book or a lecture note which covers regular matrices with all theories related to it? Any assistance will be much appreciated. (By regular I mean some power of the matrix is ...
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### Geometry of Commuting Hermitian Matrices

I am a physicist working on a project dedicated to the quantisation of commuting matrix models. In the appropriate formalism this problem is reduced to a quantisation in a curved space -- the space of ...
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### Reference request for positive matrices

I would much appreciate someone suggest me a text book which covers stochastic matrices in depth with all relevant theories.Thanks
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### Good source for self study of matrix decompositions

What is a good source for study of various types of matrix decomposition, which is both comprehensive and also includes applications? It should at least cover LU, RQ, SVD, spectral, Schur, and ...
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### The Determinant of a Sum of Matrices

Given $N$ $n \times n$ matrices $\mathsf{A}^{1}, \dots, \mathsf{A}^{N}$, \begin{align} \det \left( \sum_{i = 1}^{N} \mathsf{A}^{i} \right) = \sum_{\sigma \in S} \det \mathsf{A}^{\sigma}, \end{align} ...
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### Ring of Row Finite matrices

I need to study rings of row finite matrices. But I can not find a book that exposes this theory. Can someone recommend me a good book to this theory?
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### Require brilliant resources to self teach.

I'm far from the level of mathematical knowledge every user on this website posseses, however I am very much determined to get there as my love for mathematics increases. These are the topics: ...