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Prove that $cond(A)\ge \frac{||A||}{||A-B||}$ for any induced matrix norm

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#matrices #normed-spaces #condition-number #matrix-norms
327
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Can an upperbound constraint on the squared Frobenius norm of a matrix be expressed as a linear matrix inequality?

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#trace #linear-matrix-inequality #matrix-norms
114
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Matrix norm for two matrices simultaneously close to spectral radius

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#linear-algebra #matrices #spectral-radius #matrix-norms
734
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Proof of infinity matrix norm

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#matrices #matrix-norms
6.6k
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Proving the infinity norm is equal to the maximum value of the vector

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#vectors #normed-spaces #matrix-norms
1.7k
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About subgradient of matrix norm

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#linear-algebra #matrices #convex-analysis #subgradient #matrix-norms
182
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Norms of vectors and $1\times n$ matrices

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#linear-algebra #matrix-norms
367
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Example of application of hilbert-schmidt norm

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#linear-algebra #matrix-norms
83
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Derive Lipschitz norm equality.

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#lipschitz-functions #matrix-norms #spectral-norm
746
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Minimization of norm distance using SDPs, cone programming, etc.

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#matrices #convex-analysis #convex-optimization #semidefinite-programming #matrix-norms
275
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What are the definitions of the Matrix norms?

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#linear-algebra #normed-spaces #matrix-norms
638
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Spectral norm of matrices with complex eigenvalues

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#linear-algebra #eigenvalues-eigenvectors #normed-spaces #singular-values #matrix-norms
94
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When is $\|\boldsymbol A\| \|\boldsymbol A^{-1}\|$ bounded?

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#matrices #normed-spaces #symmetric-matrices #matrix-norms
59
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Example of a matrix where equality occurs for the relation between infinite and 2 norm

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#matrices #normed-spaces #examples-counterexamples #matrix-norms #spectral-norm
409
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Show that $\|Ax\|_2^2 = \lambda \|x\|_2^2$

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#eigenvalues-eigenvectors #normed-spaces #matrix-norms

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