In mathematics, suppose C is a collection of mathematical objects (for instance sets or functions). Then we say that C is rigid if every c ∈ C is uniquely determined by less information about c than one would expect.
It should emphasized that the above definition does not define a mathematical object. Instead, it describes in what sense the adjective rigid is typically used in mathematics, by mathematicians.
Some examples include:
- Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values.
- By the fundamental theorem of algebra, polynomials in C are rigid in the sense that any polynomial is completely determined by its values on any countably infinite set, say N, or the unit disk.
- Linear maps L(X,Y) between vector spaces X, Y are rigid in the sense that any L ∈ L(X,Y) is completely determined by its values on any set of basis vectors of X.
- Mostow's rigidity theorem