What is an orthogonal matrix?
Essentially an orthogonal
It preserves distances between points.
An orthogonal matrix is one whose inverse is equal to its transpose.
#R_theta = ((cos theta, sin theta), (-sin theta, cos theta))#
The rows of an orthogonal matrix form an orthogonal set of unit vectors. For example,
#vecA cdot vecB = -sinthetacostheta + sinthetacostheta = 0#
#||vecA|| = sqrt(cos^2theta + sin^2theta) = 1#
#||vecB|| = sqrt((-sintheta)^2 + cos^2theta) = 1#
(hence, unit vectors)
The columns also form an orthogonal set of unit vectors.
The determinant of an orthogonal matrix will always be