A group of nonsingular matrices includes A B and A -1 if it includes A and B. "Products
Chapter 6, Problem 32(choose chapter or problem)
A group of nonsingular matrices includes A B and A -1 if it includes A and B. "Products and inverses stay in the group." Which of these are groups (as in 2.7.37)? Invent a "subgroup" of two of these groups (not I by itself = the smallest group). (a) Positive definite symmetric matrices A. (b) Orthogonal matrices Q. (c) All exponentials etA of a fixed matrix A. (d) Matrices P with positive eigenvalues. (e) Matrices D with determinant 1.
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