rigidity
rigidity (n)
- plural
- rigidities
English Definitions:
rigidity, rigidness (noun)
the physical property of being stiff and resisting bending
inflexibility, rigidity, rigidness (noun)
the quality of being rigid and rigorously severe
rigidity (Noun)
The quality or state of being rigid; want of pliability; the quality of resisting change of form; the amount of resistance with which a body opposes change of form.
rigidity (Noun)
Stiffness of appearance or manner; want of ease or elegance.
rigidity (Noun)
In Economics: synonym for stickiness (of prices/wages etc.). Describing the tendency of prices and money wages to adjust to changes in the economy with a certain delay.
Rigidity
In mathematics, a rigid collection C of mathematical objects is one in which every c ∈ C is uniquely determined by less information about c than one would expect. The above statement does not define a mathematical property. 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. ⁕Holomorphic functions are determined by the set of all derivatives at a single point. A smooth function from the real line to the complex plane is not, in general, determined by all its derivatives at a single point, but it is if we require additionally that it be possible to extend the function to one on a neighbourhood of the real line in the complex plane. The Schwarz lemma is an example of such a rigidity theorem. ⁕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 infinite set, say N, or the unit disk. Note that by the previous example, a polynomial is also determined within the set of holomorphic functions by the finite set of its non-zero derivatives at any single point.
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