psmall

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 modulus < 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]=psmall(A,2.5,'d');
spec(M*A*Q)
[Q1,M1]=fullrf(eye()-Q*M);
spec(M1*A*Q1)

See also

• pbig — eigen-projection
• proj — projection
• projspec — spectral operators

Used Functions

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