Thread: Orthogonal Matrices

why are orthogonal matrices important?

Because they are easy! More generally, we can think of any matrix as the "change of basis" matrix showing how the components of a vector change if you change from one basis to another. In particular, an orthogonal matrix is a "change of basis" matrix where both bases are "orthonormal" (all basis vectors have length 1 and are orthogonal to one another) and those are particularly simple bases.

From an applications standpoint, orthogonal matrices are important because rotations of a vector can be represented by an orthogonal matrix.