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Inequality regarding diagonal entries and eigenvalues of a PSD matrix

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#linear-algebra #inequality #eigenvalues-eigenvectors #positive-semidefinite #matrix-analysis
390
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"Almost Normal" Matrix and Gap between Spectral Radius/Norm

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#matrices #matrix-norms #spectral-radius #matrix-analysis #spectral-norm
108
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Which of the statements is/are TRUE?

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#matrices #functional-analysis #normed-spaces #matrix-analysis #infinite-matrices
55
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Trace of a Summation of Positive Definite Matrices with a Real Coefficient

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#linear-algebra #matrices #trace #positive-definite #matrix-analysis
3.1k
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Index of a Nilpotent matrix

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#linear-algebra #matrices #ring-theory #nilpotence #matrix-analysis
184
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Trace of a Summation of Positive Definite Matrices

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#linear-algebra #matrices #positive-definite #matrix-analysis
1.2k
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Do eigenvalues depend smoothly on the matrix elements of a diagonalizable matrix?

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#real-analysis #linear-algebra #matrices #eigenvalues-eigenvectors #matrix-analysis
222
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Numerical radius of $2 \times 2$ complex matrix

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#matrices #functional-analysis #operator-theory #operator-algebras #matrix-analysis
1k
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Matrix exponential is continuous

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#matrices #continuity #matrix-calculus #matrix-exponential #matrix-analysis
51
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Sufficient condition for total nonnegativity

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#matrices #matrix-analysis
42
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Invariance of numerical radius

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#functional-analysis #operator-theory #operator-algebras #matrix-analysis
82
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About trace duality and other two bounds...

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#linear-algebra #matrices #convex-analysis #matrix-decomposition #matrix-analysis
281
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Equality in trace duality

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#real-analysis #linear-algebra #matrices #duality-theorems #matrix-analysis
69
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$A$ is a $12\times12$ matrix such that $A^{10 }=I$, and $\operatorname{rank}(A-I)=5$. How can we show $\operatorname{rank}(A^2 +A+I)\leq 7$?

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#linear-algebra #matrices #matrix-analysis
90
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Real Hadamard powers of matrices

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#matrices #hadamard-product #matrix-analysis

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