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onto

Every vector in the codomain is hit by at least one input; surjective.

T:V\to W is onto (surjective) when every vector of the codomain is hit at least once — exactly the statement \operatorname{im}(T)=W. One-to-one and onto are logically independent: a transformation can have either without the other, both, or neither.

See also

one-to-one image invertible transformation
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