# tut10 - on V is a real linear mapping J V → V satisfying...

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Math 235 Tutorial 10 Problems 1: Diagonalize A = - 1 2 - 2 - 2 - 1 - 1 4 - 2 5 over C . 2: Prove that if ~ z is an eigenvector of a matrix A with complex entries, then ~ z is an eigenvector of A . What is the corresponding eigenvalue? 3: Suppose that a real 2 × 2 matrix A has 1 + i as an eigenvalue with a corresponding eigenvector ± 2 i ² . Determine A . 4: Let V be a real vector space. A complex structure
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Unformatted text preview: on V is a real linear mapping J : V → V satisfying J 2 =-Id where Id is the identity mapping. Prove that under the addition operation of V and scalar multiplication deﬁned by ( a + bi ) ~x = a~x + bJ ( ~x ) for all a + bi ∈ C and ~x ∈ V , that V becomes a complex vector space. 1...
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