Skip to main content
MathOverflow

Return to Question

clarification of the comment on non-singularity is given.
Source Link
Arun
Arun
  • 745
  • 3
  • 9

Here by orthogonal matrix I mean just the rows are mutually orthogonal. Two such matrices are equivalent if one can be obtained from the other by permutations of rows and columns, or change of signs of rows and columns. I would like to know about the number of such nonequivalent $n \times n$ non-singular matrices in terms of the dimension $n$. A good lower or upper bound is also welcome.

Here by orthogonal matrix I mean just the rows are mutually orthogonal. Two such matrices are equivalent if one can be obtained from the other by permutations of rows and columns, or change of signs of rows and columns. I would like to know about the number of such nonequivalent $n \times n$ matrices in terms of the dimension $n$. A good lower or upper bound is also welcome.

Here by orthogonal matrix I mean just the rows are mutually orthogonal. Two such matrices are equivalent if one can be obtained from the other by permutations of rows and columns, or change of signs of rows and columns. I would like to know about the number of such nonequivalent $n \times n$ non-singular matrices in terms of the dimension $n$. A good lower or upper bound is also welcome.

Source Link
Arun
Arun
  • 745
  • 3
  • 9

How many orthogonal matrices (not orthonormal) are there with entries in $\{0,1,−1\}$?

Here by orthogonal matrix I mean just the rows are mutually orthogonal. Two such matrices are equivalent if one can be obtained from the other by permutations of rows and columns, or change of signs of rows and columns. I would like to know about the number of such nonequivalent $n \times n$ matrices in terms of the dimension $n$. A good lower or upper bound is also welcome.