# Questions tagged [matrices]

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate and adjoint, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), invariant factors, quadratic forms, etc. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

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### Moments of a complex matrix

How can I have higher order moments, for example, the skewness of a complex matrix, in terms of the trace and eigenvalues? As in this paper https://doi.org/10.1016/0024-3795(80)90258-X, they ...
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### Change of basis in homogeneous coordinates

I am currently trying to understand the following Python code which computes a 3D rotation-translation matrix in homogeneous coordinates : ...
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### How to mathematically model in MATLAB?

I am trying to create a code for the following statement in MATLAB: Suppose there are 60 small base stations (small mobile towers) and 1 Macro base station (big mobile tower). Let us index these nodes ...
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### Positive Definite Operators

Consider the symmetric linear operator A, for which its eigenvectors form a complete orthogonal set and all its eigenvalues are positive. Show that A is a positive definite operator. Show that the ...
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Given the finite set of matrices $\Bbb X := \{ {\bf X}_1, {\bf X}_2, \dots, {\bf X}_N \} \subset \mathbb{C}^{N_t \times L}$ and the matrix ${\bf Y} \in \mathbb{C}^{N_r \times L}$, $$\left( \hat{H}, \... 2 votes 1 answer 54 views ### Comparative statics in linear programming Suppose \Phi is a 3 \times 3 non-negative matrix and let \mu(\Phi) be a solution to the following maximization problem over a nonnegative matrix,$$\begin{aligned} \max_{(\mu_{ij}) \geq 0}& &...
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As the Wikipedia page on matrix completion states, One of the variants of the matrix completion problem is to find the lowest rank matrix $X$ which matches the matrix $M$, which we wish to recover, ...
Let $\mathbf{A} \in \mathbb{C}^{n \times n}$ be a normal matrix with eigenvalues $\lambda_1, \dots, \lambda_n$. Show there exists a permutation $\pi$ of $1, \dots n$ so that  \sum_{i=1}^n\left|a_{i ...