surjective

• Jan 11th 2012, 05:38 AM
aaaa202
surjective
Can a linear mapping ever be surjective? I can't come up with an example.
• Jan 11th 2012, 06:23 AM
Siron
Re: surjective
$f: \mathbb{R} \to \mathbb{R}: x\mapsto x$
• Jan 11th 2012, 06:37 AM
Swlabr
Re: surjective
Quote:

Originally Posted by aaaa202
Can a linear mapping ever be surjective? I can't come up with an example.

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.