# 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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### Approximating singular values of the resolvent matrix for a non-Hermitian matrix

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### Characterizing a variant of completely-Q matrices in linear complementarity problems

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### The rank of the Hadamard product

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### Operator norm of difference of matrix decompositions

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### Meaning of $K'[\cdot]$ when $K$ is an symmetric Onsager (matrix) operator

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### Uniform continuity of Cholesky decomposition

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### Projecting matrix from LDL^T factorization

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### Kulkarni-Nomizu square root of the Riemann tensor

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### System of matrix equations

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### Derivative of log determinant [closed]

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### Is there a specific name for this optimization problem?

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### Upper bound on the size of vectors contained in an ellipsoid?

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### Matrix equation involving quadratic form

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### Growth of the number of columns $j=1,\dotsc,p$ such that $\|Ae_j\|_1 > p^\alpha$ for symmetric $A$ with bounded spectrum?

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### Multiplication of two Pauli string

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### Derivative of Cholesky Factor not invertible

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### Distance of low-rank matrices to the identity for the $\infty$-norm

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### Stationary distribution of a weighted directed acyclic graph

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### Solving a fully nonlinear first order PDE

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### Gradient Descent for Markov Dynamics [closed]

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### Square root of a circulant matrix block

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### References for matrix variational problems on the unitary group

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### State-dependent positive definite matrix

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### Is a basis that almost diagonalizes a matrix 'close' to its eigenbasis?

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### Proof negative-definiteness of a nonsymmetric and rank-deficient matrix

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### Infinite positive matrices with probability eigenvector

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### How do you solve this quadratic matrix equation?

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### The d(abc)-theorem, the abc-conjecture and positive definite kernels over the natural numbers?

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### How to design a matrix function to meet the following conditions

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### If $x \ge 0$ and $\mathbf{1}^Tx \le \|x\|^2$ then $\mathbf{1}^T(I - xx^T / \|x\|^2) \mathbf{1} \ge \| [\mathbf{1} - x]_+ \|^2$

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### Uniform smoothness inequality for Schatten norms

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### Parseval's equivalent of Norm that includes a Projection matrix

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### Growth of eigenvalues for certain sequences of matrices

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### Counting eigenvalues without diagonalizing a matrix

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### Is this lower bound on the singular values of the sum of two matrices correct?

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### A lower-bound on matrix-function with vector product

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### Expectation of random matrix (minimum positive eigenvalue)

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### Follow up: Show that these vectors are linearly independent almost surely

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### Characterize matrix range

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### Show that these vectors are linearly independent almost surely

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### L_q matrix inequality

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### Can anything be said about $X^T C X$ based on the structure of $C$?

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### $A\geq B\Rightarrow A^{-1}\leq B^{-1}$ entrywise for pos.def. symmetric matrices?

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### How to find upper and lower bound

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### Bounding Frobenius norm of pseudo-inverse

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### Condition number for a symmetric positive definite matrix

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### Identify an ordered-eigenvalue simplex with tetrahedral dihedral angle $\cos ^{-1}\left(\frac{1}{3}\right)$ in volume, area formulas

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### Necessary conditions for existence of linear combination of these matrices to be singular

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### Approximation bounds for matrix multiplication

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