Rank minimization of a block matrix
$begingroup$
When is the matrix $A = begin{bmatrix}B & C \X & D end{bmatrix}$ have the minimal rank for given matrices B,C, and D? (matrices B, C, X and D have the size of $mtimes n$, $mtimes k$, $ltimes n$, and $ltimes k$).
I can "solve" the problem if $m=n=k=l$ by multiplying the matrix A to $ begin{bmatrix}D^T & C^T \-X^T & D^T end{bmatrix}$. Any ideas? Thanks.
linear-algebra matrices matrix-rank
edited Dec 1 '18 at 0:39
Bernard
119k740113
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
$endgroup$
add a comment |
$begingroup$
When is the matrix $A = begin{bmatrix}B & C \X & D end{bmatrix}$ have the minimal rank for given matrices B,C, and D? (matrices B, C, X and D have the size of $mtimes n$, $mtimes k$, $ltimes n$, and $ltimes k$).
I can "solve" the problem if $m=n=k=l$ by multiplying the matrix A to $ begin{bmatrix}D^T & C^T \-X^T & D^T end{bmatrix}$. Any ideas? Thanks.
linear-algebra matrices matrix-rank
edited Dec 1 '18 at 0:39
Bernard
119k740113
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
$endgroup$
add a comment |
$begingroup$
When is the matrix $A = begin{bmatrix}B & C \X & D end{bmatrix}$ have the minimal rank for given matrices B,C, and D? (matrices B, C, X and D have the size of $mtimes n$, $mtimes k$, $ltimes n$, and $ltimes k$).
I can "solve" the problem if $m=n=k=l$ by multiplying the matrix A to $ begin{bmatrix}D^T & C^T \-X^T & D^T end{bmatrix}$. Any ideas? Thanks.
linear-algebra matrices matrix-rank
edited Dec 1 '18 at 0:39
Bernard
119k740113
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
$endgroup$
When is the matrix $A = begin{bmatrix}B & C \X & D end{bmatrix}$ have the minimal rank for given matrices B,C, and D? (matrices B, C, X and D have the size of $mtimes n$, $mtimes k$, $ltimes n$, and $ltimes k$).
I can "solve" the problem if $m=n=k=l$ by multiplying the matrix A to $ begin{bmatrix}D^T & C^T \-X^T & D^T end{bmatrix}$. Any ideas? Thanks.
linear-algebra matrices matrix-rank
linear-algebra matrices matrix-rank
edited Dec 1 '18 at 0:39
Bernard
119k740113
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
edited Dec 1 '18 at 0:39
Bernard
119k740113
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
edited Dec 1 '18 at 0:39
Bernard
119k740113
edited Dec 1 '18 at 0:39
Bernard
119k740113
edited Dec 1 '18 at 0:39
Bernard
119k740113
119k740113
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
asked Dec 1 '18 at 0:26
magzhanmagzhan
84
84
add a comment |
add a comment |
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