The dimension of the domain of a surjective linear transformation is at least the dimension of the codomain.

Created almost 9 years ago, updated about 8 hours ago

For a surjective linear map $T:V\to W$ between finite-dimensional spaces, $\dim V\ge\dim W$. Surjectivity gives rank $\dim W$, and rank cannot exceed $\dim V$. A smaller finite coordinate space cannot linearly cover a larger one.

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