Abstract
In this paper the semiaxes of quadrics which touch each other are investigated. If two quadrics Q, Q′ are given, it turns out that we can rotate Q′ such that it touches Q in two opposite points if and only if the squared semiaxes of Q, Q′ do not separate each other. This is equivalent to the statement that for two symmetric matrices A,B there is an orthogonal matrix S with det(A — S TBS) = 0 if and only if the eigenvalues of A and B do not separate each other.
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Wallner, J. On the semiaxes of touching quadrics. Results. Math. 36, 373–383 (1999). https://doi.org/10.1007/BF03322124
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DOI: https://doi.org/10.1007/BF03322124