Microworld: Matrix
Groups
Click the Hyperlink
above to visit the Microworld.
Authors:
Kate
Johnson and
J.T.
Ratnanather
Now
that you have an idea of what a group is and what some of its properties are,
we can move on to a specific kind of group. A collection of matrices can form
a group in the same way that a collection of individual numbers can form a
group.
A
Matrix Group is just a group with some other special qualities.
Definition: Matrix Groups
A
Matrix Group is a collection of square matrices that satisfies the group properties.
The group composition is matrix multiplication, and the group inverse is the
matrix inverse. These properties are in addition to those that define all
groups (closure, associativity, existence of identity, and existence of inverses).
See the Microworld, "Introduction to Group Theory", for a review of these
properties.
Number
of Pages: 4
Animation: Yes
Grade Level:15-16
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