# Questions tagged [matrix-analysis]

The study of the properties of real and complex matrices that are more close to analysis and operator theory. For instance: the properties of positive definite matrices, matrix inequalities, perturbation analysis, matrix functions, inequalities between eigenvectors and singular values, majorization.

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### The rank of the Hadamard product

For matrices $D\in C^{d×p}$ and $E\in C^{d×p}$ with $d>p$, if $D$ is a full column matrix, for what condition that $D \odot E$ is also a full column matrix where $\odot$ denotes the Hadamard ...
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### Is this lower bound on the singular values of the sum of two matrices correct?

Equation 7 of this paper (Ramazan Türkmen, Zübeyde Ulukök, Inequalities for Singular Values of Positive Semidefinite Block Matrices, International Mathematical Forum, Vol. 6, 2011, no. 31, 1535 - 1545)...
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### A lower-bound on matrix-function with vector product

I am currently trying to show that a sequence of homeomorphisms converges to some limiting homeomorphism using Anderson's the inductive convergence criterion. However I can't explicitly compute the ...
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### Bounding Frobenius norm of pseudo-inverse

$\DeclareMathOperator{\F}{\mathrm{F}}$Let $\mathbf{A}$ and $\mathbf{A}^\prime$ be two $m\times n$ matrix such that $\|\mathbf{A}-\mathbf{A}^\prime\|_{\F}\leq \delta$. Is there any bound for the ...
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### Condition number for a symmetric positive definite matrix

I am trying to get an estimate for the induced 2-norm condition number $\kappa_{2}(M)$ of this matrix $M$: M_{ij} = \frac{1}{(n-i)!(n-j)!(2n-i-j+1)} = \displaystyle\int_{0}^{1}\frac{x^{n-i}}{(n-i)!} ...
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### Identify an ordered-eigenvalue simplex with tetrahedral dihedral angle $\cos ^{-1}\left(\frac{1}{3}\right)$ in volume, area formulas

Let us order the four eigenvalues ($\lambda_1 \geq \lambda_2 \geq \lambda_3 \geq \lambda_4$, $\Sigma_{i-1}^4 \lambda_i=1$) of a Hermitian, trace-one, positive-definite $4 \times 4$ matrix $\rho$ (a “...
I'm doing some research in Control theory, and a stumbled with this problem. Any help is appreciated. QUESTION Let $P_1,\dots,P_m$ be $m$ symmetric positive definite $n\times n$ matrices with $m<n$ ...