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Scilab help >> Linear Algebra > pbig

# pbig

eigen-projection

### Calling Sequence

[Q,M]=pbig(A,thres,flag)

### 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)

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

F. D. (1988); ;

### Used Functions

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

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