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A function f:XāYf:X\to Yf:XāY is injective or one-to-one if whenever x,yāXx,y\in Xx,yāX are such that f(x)=f(y)f(x)=f(y)f(x)=f(y), then x=yx=yx=y.
Bijective
Rank
Dimensionality & Linear Maps
Injectivity, surjectivity, and isomorphism are equivalent when Dimension is the Same
Linear Map is Injective iff Kernel is 0
Nonsingular Code
Uniquely Decodable