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Matrix norm definition with constraint

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#matrices #matrix-norms
87
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Norm ratio: find the impact of diagonal pertubations

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#matrices #matrix-norms
78
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If $A$ is a positive semi-definite matrix, is $\left\|I-\frac{A}{\|A\|}\right\|\leq 1$?

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#linear-algebra #matrices #symmetric-matrices #positive-semidefinite #matrix-norms
117
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Need a way to find $a,b$ for the vector $x' = ax + by$ such that for a matrix $A$ of size $ m \times n$, $Ax'$ is orthogonal to $Ay$

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#matrices #vectors #algorithms #matrix-norms
98
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Proving that the norm $n \|A\|_{l_\infty}$ is a matrix norm.

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#linear-algebra #matrices #normed-spaces #matrix-calculus #matrix-norms
84
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Maximal spectral norm of balanced $\pm 1$ matrix

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#matrices #discrete-optimization #bipartite-graphs #matrix-norms #spectral-norm
108
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Properties of SPD Matrix Norms

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#linear-algebra #matrices #matrix-norms
115
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Proof of the variational formulation of the nuclear norm

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#linear-algebra #matrices #matrix-norms #nuclear-norm
123
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For a symmetric matrix $A$, $\|A\|_2 \leq \|A\|_{\infty}$?

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#linear-algebra #matrices #normed-spaces #symmetric-matrices #matrix-norms
77
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Prove vector norm inequalities and use the Schwarz Inequality to confirm ratio bound

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#linear-algebra #inequality #cauchy-schwarz-inequality #matrix-norms
101
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If $L$ is a positive semi-definite matrix and all elements in each row add up to 0, How to prove that the inf-norm of $(I+L)(I+L+L^2)^{-1} \leq 1$?

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#matrices #matrix-norms #condition-number
87
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What is the "matrix-norm" of a vector?

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#linear-algebra #matrices #matrix-norms
113
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Prove that there is a rank one matrix $B$ so that $Bx = y$ where $B$ has matrix norm $1$

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#linear-algebra #matrices #matrix-rank #matrix-norms #rank-1-matrices
98
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How to minimize $\| x {\bf I} - {\bf A} \|_2$?

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#matrices #optimization #matrix-norms #spectral-norm
111
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Norm of sum of positive matrices versus the sum of norms

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#linear-algebra #inequality #positive-definite #positive-semidefinite #matrix-norms

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