The eigenfunction system corresponding to the Linear Stability Theory (LST) equations is discussed from the perspective of a basis for the eigenfunction expansion method for the Linearized Navier-Stokes Equations (LNSE). The method may lead to an infinite system of coupled ODEs or integro-differential equations. An approximation/truncation is needed to solve an initial boundary-value problem for linearized Navier-Stokes equations using this method. Examples include coupling of modes due to weakly nonparallel flow effect, scattering of an acoustic wave on a localized roughness, initial-value problem for perturbations in boundary layers, distributed forcing due to impinging particulates or thermal noise, and an actuator located on a wall. The BiGlobal/TriGlobal system of eigenfunctions can also be used for solving the Linearized Navier-Stokes equations in other complex flows along the same lines of the eigenfunction expansion method.