Why is orthogonal transformation also called unitary transformation?
Orthogonal transformation originally came from Wikipedia, and this matrix element is called normal coordinate. The kinetic energy, potential energy and potential energy of molecular internal motion expressed by mass-weighted coordinates can be known from the mathematical expression of force constant, so the matrix is an orthogonal transformation, and the matrix can be transformed into a diagonal matrix through unitary transformation. Then, every matrix element is a linear combination of all the mass-weighted coordinates of the molecule, and the total number of matrix elements is exactly equal to the number of mass-weighted coordinates, so these matrix elements are called normal coordinates, and the potential energy of the molecule in these transformations is constant, so the orthogonal transformation is also called unitary transformation.