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brru25
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If p is prime, prove that for every function f: Fp -> Fp there exists a polynomial Q (depending on f) of degree at most p-1 such that f(x) = Q(x) for each x in Fp.
Have you tried it? What happened?brru25 said:Would polynomial interpolation work here?
Polynomial interpolation works over any field... or is there something else you see that I don't?HallsofIvy said:I don't see how you could interpolate.
Well, I think of "interpolation" as finding values between given values. And since this is a finite field, there is nothing "between" values.Hurkyl said:Polynomial interpolation works over any field... or is there something else you see that I don't?
http://en.wikipedia.org/wiki/Polynomial_interpolationHallsofIvy said:Well, I think of "interpolation" as finding values between given values. And since this is a finite field, there is nothing "between" values.
A linear map is a mathematical function that preserves the structure of vector spaces. It is also known as a linear transformation or a linear operator.
In the context of a linear map, "degree P-1" refers to the degree of the polynomial that represents the map. It represents the highest power of the independent variable in the polynomial.
A linear map is a type of function, but it has certain properties that make it different from a regular function. For example, a linear map preserves the operations of addition and scalar multiplication, while a regular function may not.
The degree of a linear map is important because it determines the dimension of the vector space that the map is operating on. It also affects the behavior and properties of the map, such as whether it is invertible or not.
Linear maps are used in a variety of scientific fields, such as physics, engineering, and economics, to model and analyze relationships between variables. They are also used in data analysis and machine learning algorithms.