# What is an orthogonal matrix?

##### 1 Answer

#### Answer:

Essentially an orthogonal

It preserves distances between points.

#### Explanation:

An orthogonal matrix is one whose inverse is equal to its transpose.

A typical

#R_theta = ((cos theta, sin theta), (-sin theta, cos theta))#

for some

The rows of an orthogonal matrix form an orthogonal set of unit vectors. For example,

#vecA cdot vecB = -sinthetacostheta + sinthetacostheta = 0#

(hence, orthogonal)

#||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 *special orthogonal matrix*.