|
2 | added 20 characters in body | ||
|
Let $M$ be a $2^n \times 2^n$ matrix over real number field, where the rows and columns are indexed by subsets of $[n] := {1,2,\ldots,n}$, and defined as follows, $ M_{A, B} = 1 $ if $A \subseteq B$; $M_{A, B} = -1$ if $B \subsetneq A$; $M_{A, B}$ is undefined otherwise.can take arbitrary value over $\mathbb{R}$. In words, $M$ is a matrix with some missing entries. Is there some result lower bounds the rank of matrix $M$, for example, $rk(M) \ge n^{\Omega(\log n)}$. |
||||
|
|
1 |
|
||
Rank of a matrix with missing entriesLet $M$ be a $2^n \times 2^n$ matrix over real number field, where the rows and columns are indexed by subsets of $[n] := {1,2,\ldots,n}$, and defined as follows, $ M_{A, B} = 1 $ if $A \subseteq B$; $M_{A, B} = -1$ if $B \subsetneq A$; $M_{A, B}$ is undefined otherwise. In words, $M$ is a matrix with some missing entries. Is there some result lower bounds the rank of matrix $M$, for example, $rk(M) \ge n^{\Omega(\log n)}$.
|
||||
