Matrix Groups

Overview

Invertible {% n \times n %} Matrices with the operation of multiplication form a group.

Axioms

• Closure - two Invertible {% n \times n %} matrices multiplied together returns an invertible {% n \times n %} matrix.
  {% AB = C %}
• Associativity
  {% A(BC) = (AB)C %}
• Identity - the matrix of zeros with ones along the diagonal is the multiplicative identity
• Inverse - each element has an inverse, by assumption

Matrix Lie Groups

• Rotation Group