
Math 4373 Homework
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Homework
[HK] stands for HoffmanKunze, [H] stands for Halmos.
 Fields [Due Tuesday 5th Sept]

 Verify that the complex numbers form a field.
 [H] page 2, questions 1,5,6,7.
 Prove that the set of all constructibele numbers is a field.
 Vector spaces and subspaces [Due Tuesday 5th Sept]

 [H] pge 6: questions 2,4,5
 [HK] section 2.1: questions 5, 7
 [HK] section 2.2: questions 1,2,4,6,8,9
 Show that the space of nbyn matrices is
the sum of the space of
skewsymmetric
matrices and the space of symmetric matrices.
 Bases and dimension (Due Tuesday, Sept. 12)

 [H] section 7: questions 6, 7.
 [H] section 8: questions 1,3.
 [HK] section 2.3: questions 9, 12, 14.
 Linear Transformations and Matrices;
isometries of the euclidean plane (Due Tuesday, Oct. 10)

 [HK] section 3.2: questions 7, 8, 11.
 [HK] section 3.3: question 3.
 [HK] section 3.4: questions 6, 8 (definition on page 94), 9, 12.
 Write down explicit coordinate map (x,y) > (?, ?) for the
isometry consisting of rotation about the point (2,3) through Pi radians.
 Show that matrix multiplication of the (3X3)matrices
discovered in class
corresponds to composition of euclidean isometries.








