Orthogonal Transformation: the transformation that preserve distance and origin
represented by matrices Q^T Q = I
Rotation: additionally preserve orientation (\det Q > 0)
Reflection: reverse orientation (\det Q < 0)
Scaling: preserve direction while change magnitude
Negative Scaling: a sequence of reflections (how many reflections depends on the dimension of the space)
in 2D: Negative Scaling is Rotation
in 3D: Negative Scaling is Reflection
Symmetric Matrix: a matrix A such that A = A^T.
Nonuniform Scaling: a symmetric matrix A := R^TDR
rotate to new axes (R)
apply a diagonal scaling (D)
rotate back to original axes (R^T)
Spectral Theeorem: all symmetric matrix represent nonuniform scaling
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