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Results tagged with matrix-analysis
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user 8435
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.
0
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3
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621
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Maximizing/Minimizing the Operator norms of 0-1 matrices subject to a constraint
Fix $n$ and let $B, C$ be two $n \times n$ 0-1 matrices of full rank such that $\sum_{i,j} b_{i,j}^2 = \sum_{i,j} c_{i,j}^2$, in other words they have the same number of $0$ entries and the same numbe …
- 3,699
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votes
1
answer
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Counting Boolean Normal Matrices of size $2n \times 2n$
Fix $n$ a natural number. Consider the set of all $2n \times 2n$ matrices with entries from {0,1}. This is clearly a finite set. I would like to count the number of such normal matrices for fixed $ …
- 3,699
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Norm of triangular truncation operator on rank deficient matrices
Fix $r \geq 1$ and let $A_n$ be the $n \times n$ identity matrix with the bottom $n-r$ rows replaced with rows of zeros. Then $||A_n|| = 1$ for all $n$ and $||T_n \circ A_n|| = ||A_n||$ so we have th …
- 3,699