Can a linear mapping ever be surjective? I can't come up with an example.

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- Jan 11th 2012, 04:38 AMaaaa202surjective
Can a linear mapping ever be surjective? I can't come up with an example.

- Jan 11th 2012, 05:23 AMSironRe: surjective
What about:

$\displaystyle f: \mathbb{R} \to \mathbb{R}: x\mapsto x$ - Jan 11th 2012, 05:37 AMSwlabrRe: surjective
Linear transformations

*are*matrices, and a matrix is invertible if and only if it is square with non-zero determinant. That is, matrices with non-zero determinant*are*bijective linear transformations. So every invertible matrix corresponds to a surjective linear map.

(...for a suitable value of*are*...)

If you want, you could try and use matrices to classify all surjective linear maps. It is a good exercise, methinks.