# Questions tagged [matrices]

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 tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.

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### Equivalent definition of positive semidefinite

I am reading a paper which repetitively uses the following statement, but I don't know why this is true: Statement Let $A$ be a symmetric $n$-by-$n$ matrix, and $B$ be a $n$-by-$n$ matrix, $A\geq 0$ ...
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### Construction of skew-Hadamard matrix of order 292

I am currently looking into how to construct a skew-Hadamard matrix of order 292. Where can I find such construction? According to multiple papers (e.g. Koukouvinos and Stylianou - On skew-Hadamard ...
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### Conjecture on the existence of centrosymmetric Hadamard matrices

I work with centrosymmetric matrices and recently have started exploring the question of the existence of centrosymmetric Hadamard matrices. Definition: An $n \times m$ matrix $A = (a_{i,j})$ is ...
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### Results on Boolean matrices

Matrices with entries in the finite field of two elements $\mathbb{F}_2$, and with the usual operations of matrix addition and multiplication, have been intensively studied, especially due to their ...
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Given a matrix $L\in \mathbb{R}^{3 \times 3}$, I'm looking for a method to find the closest (in a least squares sense) product of a non-uniform scaling matrix and a rotation matrix: $$\min_{s\in\... 3 votes 2 answers 407 views ### Reducing 9\times9 determinant to 3\times3 determinant Consider the 9\times 9 matrix$$M = \begin{pmatrix} i e_3 \times{} & i & 0 \\ -i & 0 & -a \times{} \\ 0 & a \times{} & 0 \end{pmatrix}$$for some vector a \in \mathbb R^3, ... • 43 1 vote 1 answer 59 views ### A question about the sign of quadratic forms on nonnegative vectors Let M be a real square matrix of order n\ge 3. Assume that for every nonnegative vector \textbf{z}\in \mathbb R^n which has at lease one zero entry we have \textbf{z}^T M \textbf{z} \ge 0. Can ... 2 votes 1 answer 128 views ### Existence of finite dimensional representation of an algebra Let m>1 be an integer and let A be the algebra generated by the elements \{u^i_j,v^i_j,\bar{u}^i_j, \bar{v}^i_j| 1\leq i,j\leq m\} quotient over the relations \begin{eqnarray} u^i_j v^k_l&... • 271 9 votes 1 answer 302 views ### One question on circulant (-1,1)-matrices Let n > 13 be a positive integer. Is there any n\times n circulant (-1,1)-matrix A satisfying the following property:$$AA^T=(n-1)I+J where $I$ is the $n\times n$ identity matrix and $J$ ...
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It might be helpful for data science/bioinformatics challenge. Consider for simplicity three rectangular matrices $Y_{true}$ , $Y_{predict0},Y_{predict1}$ of the same sizes say 70000*140. Let us ...