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Alexander Matrix

A presentation matrix for the Alexander Invariant $H_1(\tilde X)$ of a Knot $K$. If $V$ is a Seifert Matrix for a Tame Knot $K$ in ${\Bbb{S}}^3$, then $V^{\rm T}-tV$ and $V-tV^{\rm T}$ are Alexander matrices for $K$, where $V^{\rm T}$ denotes the Matrix Transpose.

See also Alexander Ideal, Alexander Invariant, Alexander Polynomial, Seifert Matrix


Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 206-207, 1976.

© 1996-9 Eric W. Weisstein