tut9 - Math 235 Tutorial 9 Problems 1 Determine a real...

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Unformatted text preview: Math 235 Tutorial 9 Problems 1: Determine a real canonical form of A = the bring the matrix into this form. 11 and give a change of basis matrix P −2 3 −1 2 −2 2: Determine a real canonical form of A = −2 −1 −1 and give a change of basis 4 −2 5 matrix P the bring the matrix into this form. 3: Suppose that a real 2 × 2 matrix A has 1 + i as an eigenvalue with a corresponding 2 eigenvector . Determine A. i 4: Let V be a real vector space. A complex structure 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 = ax + bJ (x) for all a + bi ∈ C and x ∈ V , that V becomes a complex vector space. 1 ...
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