pbig - eigen-projection
Projection on eigen-subspace associated with eigenvalues with real part >= thres ( flag='c' ) or with magnitude >= thres ( flag='d' ).
The projection is defined by Q*M , Q is full column rank, M is full row rank and M*Q=eye .
If flag='c' , the eigenvalues of M*A*Q = eigenvalues of A with real part >= thres .
If flag='d' , the eigenvalues of M*A*Q = eigenvalues of A with magnitude >= thres .
If flag='c' and if [Q1,M1] = full rank factorization ( fullrf ) of eye()-Q*M then eigenvalues of M1*A*Q1 = eigenvalues of A with real part < thres .
If flag='d' and if [Q1,M1] = full rank factorization ( fullrf ) of eye()-Q*M then eigenvalues of M1*A*Q1 = eigenvalues of A with magnitude < thres .
A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X; [Q,M]=pbig(A,1.5,'d'); spec(M*A*Q) [Q1,M1]=fullrf(eye()-Q*M); spec(M1*A*Q1)
psmall , projspec , fullrf , schur ,
F. D. (1988); ;
pbig is based on the ordered schur form (scilab function schur ).