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Line 3: == A linear map from a finite-dimensional space is always continuous == Let ''X'' and ''Y'' be two normed spaces and ''f'' a linear map from ''X'' to ''Y''. If ''X'' is [[finite-dimensional]], choose a ~~base~~basis (''e''<sub>1</sub>, ''e''<sub>2</sub>, …, ''e''<sub>''n''</sub>) in ''X'' which may be taken to be unit vectors. Then, :<math>f(x)=\sum^n_{i=1}x_if(e_i),</math> and so by the [[triangle inequality]],

Discontinuous linear map: Difference between revisions