Cryptocurrency Q&A
How to prove a transformation is injective?
How to prove a transformation is injective?
Carlo
Sun Oct 13 2024
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7 answers
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I'm trying to understand how to prove that a transformation is injective. I know it involves showing that every element of the domain maps to a unique element in the codomain, but I'm not sure how to formally demonstrate this.
7 answers
Lucia
Tue Oct 15 2024
Injectivity is a crucial characteristic in various mathematical and computational contexts, particularly in fields such as linear algebra, functional analysis, and cryptography.
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Stefano
Tue Oct 15 2024
The concept of injectivity in vector spaces involves a specific type of transformation, known as T, which maps elements from one vector space V to another vector space W.
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Stefano
Tue Oct 15 2024
Injectivity, also referred to as one-to-one mapping, holds true for T if the condition T(u) = T(v) necessarily implies that u and v are identical vectors within the domain space V.
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EchoWhisper
Tue Oct 15 2024
Essentially, this means that no two distinct vectors in V can be mapped to the same vector in W under the transformation T. Each vector in the target space W is uniquely associated with at most one vector from the domain space V.
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Michele
Tue Oct 15 2024
This property ensures that the transformation T preserves the uniqueness of vectors within the domain space as they are mapped to the target space. It avoids the scenario where multiple inputs lead to the same output.
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