Linear lumping in systems with time-scale separation

9 APPROXIMATE LUMPING IN SYSTEMS WITH TIME-SCALES SEPARATION 4.9.1 Linear lumping in systems with time-scale separation 

In Section 4.8.4 we introduced the Schur vector. We will now formalize this concept and show how the Schur matrix can be used as a lumping matrix for systems with time-scale separation. 

If A C then there exists a unitary transformation matrix Q C such that 

If (2 = [qi. q ] is a column partition of the unitary matrix Q, then the q, are referred to as Schur vectors satisfying 

Q is an orthogonal transformation so that QQ = Q Q = I making the calculation of M simple because it is the transpose of the original matrix 

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