Dual spaces and linear mappings Exercise Pullback Linear form dual mapping surjective injective

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Pi_anist Maths CA

Published on Apr 21, 2024
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In this video we deal with dual spaces and dual mappings. Let V and W be K-vector spaces and phi a linear mapping between V and W, then we prove: a) For all linear forms my from W to K, the pullback of my under phi is a linear form from V to K. b) The dual mapping from the dual space of W to the dual space of V, defined by the pullback, is linear. c) If phi is surjective, then the dual mapping is injective. linear algebra, linear, algebra, vector space, vector spaces, dual, dual space, dual spaces, linear mapping, mapping, one form, linear form, pullback, back transport, definition, exercise, solution, exam, state exam, test, dual, dual mapping, dual, surjective, injective

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