Orthogonal Matrices and Cosets (translates) of Linear Subspaces
$begingroup$
Let $M_n(F_2)$ be the vector space of all $ntimes n$ matrices over the finite field $F_2$. Let $O(n)subset M_n(F_2)$ be the set of all orthogonal matrices and $Wsubseteq O(n)$ be an affine subspace (coset of a linear subspace) of dimension $k$. What is the largest possible value of $k$? That is I want to find the largest size of affine subspaces in $O(n)$.
linear-algebra matrices orthogonal-matrices
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
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add a comment |
$begingroup$
Let $M_n(F_2)$ be the vector space of all $ntimes n$ matrices over the finite field $F_2$. Let $O(n)subset M_n(F_2)$ be the set of all orthogonal matrices and $Wsubseteq O(n)$ be an affine subspace (coset of a linear subspace) of dimension $k$. What is the largest possible value of $k$? That is I want to find the largest size of affine subspaces in $O(n)$.
linear-algebra matrices orthogonal-matrices
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
$endgroup$
add a comment |
$begingroup$
Let $M_n(F_2)$ be the vector space of all $ntimes n$ matrices over the finite field $F_2$. Let $O(n)subset M_n(F_2)$ be the set of all orthogonal matrices and $Wsubseteq O(n)$ be an affine subspace (coset of a linear subspace) of dimension $k$. What is the largest possible value of $k$? That is I want to find the largest size of affine subspaces in $O(n)$.
linear-algebra matrices orthogonal-matrices
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
$endgroup$
Let $M_n(F_2)$ be the vector space of all $ntimes n$ matrices over the finite field $F_2$. Let $O(n)subset M_n(F_2)$ be the set of all orthogonal matrices and $Wsubseteq O(n)$ be an affine subspace (coset of a linear subspace) of dimension $k$. What is the largest possible value of $k$? That is I want to find the largest size of affine subspaces in $O(n)$.
linear-algebra matrices orthogonal-matrices
linear-algebra matrices orthogonal-matrices
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
asked Dec 17 '18 at 9:58
DavitSDavitS
1114
1114
add a comment |
add a comment |
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