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Why is the constraint $\mbox{rank} (X) \leq r$ non-convex?

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#matrices #convex-optimization #matrix-rank #constraints #non-convex-optimization
45
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Matrix ranks and minors

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#matrix-rank
58
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Show that $(e_1,\dots, e_r)$ is a base of $\operatorname{im}(A) \subseteq \mathbb{K}^m$

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#linear-algebra #matrices #proof-verification #matrix-rank
621
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Dimension of a set of vectors

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#linear-algebra #vectors #matrix-rank
84
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Nullity is larger than expected, so what is the solution?

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#matrix-rank #svd #singular-values
71
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Why is it robust and perturbed in matrix completion problem?

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#linear-algebra #matrices #matrix-rank #nuclear-norm #matrix-completion
927
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Rank of the difference of two projection matrices.

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#linear-algebra #matrices #matrix-rank #projection-matrices
81
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Pure States of Multi-Matrix Algebras

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#linear-algebra #matrices #functional-analysis #matrix-rank
93
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Iterative Algorithm for increasing matrix rank

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#matrices #algorithms #matrix-rank
193
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Number of rank 1 matrices with $0/1$ entries?

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#linear-algebra #combinatorics #matrices #matrix-rank #rank-1-matrices
313
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Rank of Products of Matrices

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#linear-algebra #reference-request #matrix-rank
114
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Explicit linear relation for columns of adjugate matrix

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#linear-algebra #matrices #matrix-rank
107
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Is $\operatorname{rk}(\bar AA)=\operatorname{rk}(A^*A)$ ??

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#linear-algebra #matrices #matrix-rank
806
Views

Rank Equation for non-square Matrix

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#matrix-rank
43
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If $P$ is a $7\times7$ matrix of rank $4$ and if $\hat{a}$ be any vector in $\mathbb{R}^7$, then to find minimum rank of $S=P+\hat{a}\hat{a}^t$ .

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#linear-algebra #matrix-rank

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