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Linearly Dependent Curves

Two curves $\phi$ and $\psi$ satisfying

\begin{displaymath}
\phi+\psi=0
\end{displaymath}

are said to be linearly dependent. Similarly, $n$ curves $\phi_i$, $i=1$, ..., $n$ are said to be linearly dependent if

\begin{displaymath}
\sum_{i=1}^n \phi_i=0.
\end{displaymath}

See also Bertini's Theorem, Study's Theorem


References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 32-34, 1959.




© 1996-9 Eric W. Weisstein
1999-05-25