In the rank nullity theorem for $T \colon V \to W$, $V$ is finite dimensional. What if $V$ is infinite dimensional?

Asked Sep 07 '18 at 12:20

Active Sep 07 '18 at 12:47

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In the Sylvester rank nullity theorem, $T \colon V \to W$ is a linear transformation and $V$ is finite dimensional. What if $V$ is infinite dimensional?

This was actually asked before on this site, but I’m not satisfied with the answers. Please give me a sketch of a proof how this is true in infinite dimensions, and please give me an example for it.

edited Sep 07 '18 at 12:47

Jendrik Stelzner

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asked Sep 07 '18 at 12:20

Priya Dey

I've seen all stack querries, if you have your own please share in answer box rather comment – Priya Dey Sep 07 '18 at 12:27
4

@PriyaDey it may help your question if you go through some of the other answers to this question and explain what you found unsatisfying or difficult to understand. – Neal Sep 07 '18 at 12:50

In the rank nullity theorem for $T \colon V \to W$, $V$ is finite dimensional. What if $V$ is infinite dimensional?

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