Complex sentence: Equivalently, it is the group of "n" × "n" orthogonal matrices of a given dimension, where the group operation is given by matrix multiplication, and an orthogonal matrix is a real matrix whose inverse equals its transpose.
Split into simpler sentences: Equivalently, it is the group of orthogonal matrices of a given dimension, where the group operation is given by matrix multiplication. An orthogonal matrix is a real matrix whose inverse equals its transpose.