What is Orthogonalisation, symmetric orthogonalisation?

Orthogonalisation transforms a set of signals, on each date, into uncorrelated ones spanning the same space: sequentially (Gram–Schmidt), each signal residualised on those before it, so that the order decides who keeps the shared part; or by symmetric orthogonalisation, $Z S^{-1/2}$ with $S$ the signals’ correlation matrix, the orthonormal set closest to the original signals, a construction that goes back to Löwdin’s orthonormalisation of overlapping atomic orbitals (1950).