Let f :$ ℝ^n→ℝ^n$ be a linear transformation. Is f always continuous? Can anyone help how to show this?
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1Yes. Any linear transformation between finite dimensional vector spaces is continuous. – Oiler Dec 04 '16 at 23:05
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1Combining two proofs from two Wikipedia pages yields the result: Proof that linear maps between finite dimensional spaces are bounded. Equivalence of boundedness and continuity. – Dec 04 '16 at 23:05
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The usual (product) topology on $\mathbb{R}^n$ is assumed (I think). The continuity of linear transformations is a special case of the continuity of polynomial functions. – hardmath Dec 04 '16 at 23:49