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Parametrization of Rank at most k Matrices

Matrices with rank exactly r as varietyexistence of neighbor of linear transformation T such that…Rank $2$ matrices$textrank(Z)=p$ for almost all $ZinmathbbR^ntimes p$Full rank factorizationPolar set of orthogonal matrices set is nuclear norm ballRank of symmetric matrix.spectral value of multiple matricesAre the sets $X: max_i textRelambda_i (B+AX) < 0$ and $X: rho(B+AX) < 1$ homeomorphic?Proving that a spectral measure is additive

0

2

$begingroup$

$F:mathbbR^ntimes krightarrow mathcalMsubsetmathbbR^ntimes n$ defined by $Umapsto UU^T$ has image in the set $mathcalM = Min mathbbR^ntimes n : Msucceq 0, textrank(M)le k$. Let $delta> 0$ be arbitrarily small and equip $mathbbR^ntimes k$ and $mathbbR^ntimes n$ with the spectral norms. Is it true that the image of $B(U,delta) = V : $ under $F$ contains all of the PSD, $ntimes n$ matrices with rank at most $k$ in some ball (of any radius)?

linear-algebra

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edited Mar 29 at 22:00

user585541

asked Mar 29 at 21:54

user585541user585541

716

$endgroup$

add a comment | 

0

2

$begingroup$

$F:mathbbR^ntimes krightarrow mathcalMsubsetmathbbR^ntimes n$ defined by $Umapsto UU^T$ has image in the set $mathcalM = Min mathbbR^ntimes n : Msucceq 0, textrank(M)le k$. Let $delta> 0$ be arbitrarily small and equip $mathbbR^ntimes k$ and $mathbbR^ntimes n$ with the spectral norms. Is it true that the image of $B(U,delta) = V : $ under $F$ contains all of the PSD, $ntimes n$ matrices with rank at most $k$ in some ball (of any radius)?

linear-algebra

share|cite|improve this question

edited Mar 29 at 22:00

user585541

asked Mar 29 at 21:54

user585541user585541

716

$endgroup$

add a comment | 

$begingroup$

$F:mathbbR^ntimes krightarrow mathcalMsubsetmathbbR^ntimes n$ defined by $Umapsto UU^T$ has image in the set $mathcalM = Min mathbbR^ntimes n : Msucceq 0, textrank(M)le k$. Let $delta> 0$ be arbitrarily small and equip $mathbbR^ntimes k$ and $mathbbR^ntimes n$ with the spectral norms. Is it true that the image of $B(U,delta) = V : $ under $F$ contains all of the PSD, $ntimes n$ matrices with rank at most $k$ in some ball (of any radius)?

linear-algebra

share|cite|improve this question

edited Mar 29 at 22:00

user585541

asked Mar 29 at 21:54

user585541user585541

716

$endgroup$

share|cite|improve this question

edited Mar 29 at 22:00

user585541

asked Mar 29 at 21:54

user585541user585541

716

share|cite|improve this question

edited Mar 29 at 22:00

user585541

asked Mar 29 at 21:54

user585541user585541

716

asked Mar 29 at 21:54

user585541user585541

716

asked Mar 29 at 21:54

user585541user585541

716