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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.

2,115 questions
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How can i determine the elements of this matrix?

i am new to matrices, i am learning with a book but i am stuck at this task, i need to determine the elements of this matrix: and this is the solution : i dont understand how to get there, any help ...
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I wonder how one can study the integral orthogonal group of a given (symmetric, positive definite) bilinear form like the one described by the following matrix: $$M=\begin{bmatrix} x_1 &... 0answers 69 views Algebra of block matrices with scalar diagonals I am interested in block matrices A, that is A\in M_{n\times n}(R) where R=M_{s\times s}(k) and k is a field, such that for every positive integer m the matrix A^m has only scalar blocks ... 1answer 78 views Lipschitz property of matrix function only depending on singular values Let f be a function from \mathbb{R}^{n\times n} to \mathbb{R} such that there exists another symmetric function g (invariant under permutation of coordinates) from \mathbb{R}^{n} to \mathbb{... 0answers 57 views How to obtain mathematical expectation with the vector as random variable? In my study, I wish to get the mathematical expectation for the term below. The vector \boldsymbol{z} \in \mathcal{C}^{N\times1} and \boldsymbol z \sim \mathcal{CN}\left(\boldsymbol{0},\boldsymbol{... 0answers 63 views Generalization of Cauchy's eigenvalue interlacing theorem? Cauchy's Interlacing Theorem says that given an n \times n symmetric matrix A, let B be an (n-1) \times (n-1) principal submatrix of it, then the eigenvalues of A and those of B interlace. ... 1answer 124 views How can one integrate over the unit cube, subject to certain (quantum-information-theoretic) constraints? To begin, we have two constraints \begin{equation} C1=x>0\land z>0\land y>0\land x+2 y+3 z<1 \end{equation} and \begin{equation} C2=x>0\land y>0\land x+2 y+3 z<1\land x^2+x (3 z-2 ... 1answer 277 views Recovering “n” from M_n(\mathbb{C}) Is there an example of an infinite-dimensional C^*-algebra A which admits the following structure: The C^* algebra A admits a faithful trace tr such that the multiplication m: A\otimes A \... 2answers 477 views Does a non-singular matrix have a large minor with disjoint rows and columns and full rank? Say I have an n-by-n non-singular matrix A all of whose diagonal entries are 0. We call an m-by-m minor of A good if its set I of row indices and its set J of column indices (I,J\... 1answer 152 views Representation of 4\times4 matrices in the form of \sum B_i\otimes C_i Every matrix A\in M_4(\mathbb{R}) can be represented in the form of$$A=\sum_{i=1}^{n(A)} B_i\otimes C_i$$for B_i,C_i\in M_2(\mathbb{R}). What is the least uniform upper bound M for such n(A)... 1answer 46 views Equalities between transforms of matrices that are extremely different I have two 2N\times 2N matrices, defined by blocks:$$ A = \begin{bmatrix} a & 0 \\ 0 & 0 \end{bmatrix}  B = \begin{bmatrix} 0 & 0 \\ 0 & b \end{bmatrix}  where $a$ and $b$ ...
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Eigenvalue-taking operator?

$\newcommand{Tr}{\operatorname{Tr}}$ Is there a continuous map $(p,t) \mapsto \lambda(p,t)$ which, given a path $p: [0,1] \to M(2,\mathbb R)$ and a $t \in \mathbb [0,1]$, gives back an eigenvalue of \$...

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