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23 votes
Accepted

Existence of Rational Orthogonal Matrices

Yes. It is a theorem of Cayley that the mapping $S \rightarrow (S-I)^{-1}(S+1)$ gives a correspondence between the set of $n\times n$ skew-symmetric matrices over $\mathbb{Q}$ and the set of $n\times …
Igor Rivin's user avatar
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29 votes
Accepted

Is this 1974 claim still valid?

This claim is not valid. The big breakthrough was the paper below: MR0839134 (88c:12011) Kovacic, Jerald J. An algorithm for solving second order linear homogeneous differential equations. J. Symbo …
Igor Rivin's user avatar
  • 96.4k