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Results tagged with matrix-equations
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user 9025
Equations whose unknown is a matrix, such as, for instance, algebraic Riccati equations $XAX+XB+CX+D=0$ or matrix differential equations (e.g. $\dot X(t)=AX(t)$. This tag is *not* meant for general systems of linear equations $Ax=b$.
9
votes
Solving the matrix equation $XX^t = A$ for binary matrix $X$
For general $A,X~$ this is a very difficult problem, but the condition you give that the rows of $X~$ have sum 2 makes it much easier. Consider each row to be an edge of a graph $G~$ (i.e. the two on …
- 37.7k
9
votes
A variant of Cholesky decomposition involving binary matrices
Even the case where $B$ is constant on the diagonal and constant off the diagonal is extremely difficult. For example, it includes the question of for which orders a finite projective plane exists. If …
- 37.7k
6
votes
The number of 0-1 normal matrices
For orders 1 to 9:
2, 8, 68, 1124, 36112, 2263268, 281249824, 70329901860, 35546752694048.
I computed these numbers by finding representatives of the isomorphism classes of normal digraphs plus the …
- 37.7k
5
votes
A problem about determinant and matrix
If there is a rational nonzero solution, there is an integer nonzero solution by multiplying up. At least one of the integers can be assumed odd by dividing out a common power of two.
The determinant …
- 37.7k