University of Regina
Department of Mathematics and Statistics
MATH 401/890 Matrix Lie Groups
Winter Semester 2015
Homework Assignment no. 1 - Solutions
All vectors on this exercise sheet will be regarded as columns. If A is an n n matrix and x a
vector wi
University of Regina
Department of Mathematics and Statistics
MATH 401/890 Matrix Lie Groups Winter 2015
Homework Assignment no. 6 - Solutions
1. Do Exercise 5, page 89, in the textbook.
Solution. As mentioned in class, we have
1
1
eadX etadY = (I + adX +
University of Regina
Department of Mathematics and Statistics
MATH 401/890 Matrix Lie Groups Winter 2015
Homework Assignment no. 5 - Solutions
1. Show that any Lie group homomorphism S 1 S 1 is z z k , where k Z. (See again Denition
1.15 for the notion of
University of Regina
Department of Mathematics and Statistics
MATH 401/890 Matrix Lie Groups Winter 2015
Homework Assignment no. 4 - Solutions
1. Do Exercise 10, page 60, in the textbook. Suggestion. You may want X to be a multiple of the
identity matrix.
University of Regina
Department of Mathematics and Statistics
MATH 401/890 Matrix Lie Groups Winter 2015
Homework Assignment no. 2 - Solutions
1. [Connectedness of SO(n) for n 2 (Ex. 13, p. 25 in Hall).]
(a) Show that SO(2) consists of matrices of the for
University of Regina
Department of Mathematics and Statistics
MATH 401/890 Matrix Lie Groups Winter 2015
Homework Assignment no. 3 - Solutions
0. Read the proof of Theorem 2.7 in the textbook. Exercises 2 and 5, page 59 in the textbook are
used in that pr