pbig

Arguments

A

real square matrix

thres

real number

flag

character string ('c' or 'd')

Q,M

real matrices

Description

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.

Examples

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)

See also

• psmall — spectral projection
• projspec — spectral operators
• fullrf — full rank factorization
• schur — [ordered] Schur decomposition of matrix and pencils

Used Functions

pbig is based on the ordered schur form (scilab function schur).