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A quantity such as a Discriminant which remains unchanged under a given class of
algebraic transformations. Such invariants were originally called Hyperdeterminants by
Cayley. 
See also Discriminant (Polynomial), Invariant, Quadratic Invariant
References
Grace, J. H. and Young, A. The Algebra of Invariants. New York: Chelsea, 1965.
Gurevich, G. B. Foundations of the Theory of Algebraic Invariants. Groningen, Netherlands: P. Noordhoff, 1964.
Hermann, R. and Ackerman, M. Hilbert's Invariant Theory Papers. Brookline, MA: Math Sci Press, 1978.
Hilbert, D. Theory of Algebraic Invariants. Cambridge, England: Cambridge University Press, 1993.
Mumford, D.; Fogarty, J.; and Kirwan, F. Geometric Invariant Theory, 3rd enl. ed. New York: Springer-Verlag, 1994.
Invariants