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18 nov. 2016 Finally we will call a function bijective (also called a ... A linear transformation is injective if and only if its kernel is the trivial.



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2.2 Properties of Linear Transformations Matrices. Null Spaces and Ranges. Injective



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The subject of solving linear equations together with inequalities is studied in Math 561. I'll ignore this issue. 1. Page 2. 2. DAVID SPEYER.



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assumption u1 ? u2 = 0 hence u1 = u2 and hence s is injective. • Let s : U ?? V be a linear transformation



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If it is invertible give the inverse map. 1. The linear mapping R3 ? R3 which scales every vector by 2. Solution note: This is surjective



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En particulier injective ?.



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It is termed bijective if it is both injective and surjective. A bijective map has a unique inverse map. (3) The standard basis vector ei is the vector with a 1 



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What does it mean for f to be (a) injective (b) surjective and (c) bijective? Solution to 0.1. If you can't remember this



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Note that a square matrix A is injective (or surjective) iff it is both injective and surjective i.e.



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Understand what is meant by surjective injective and bijective