schur

schur(obj, [sort])

Computes the Schur decomposition of a square matrix.

Suppose the input is the square matrix A:

• If sort is not specified, return 2 matrices: T (Schur form of A, an upper triangular matrix) and an unitary matrix Z (the transpose matrix of Z is equal to its inverse matrix), so that A = Z*T*Z-1.
• If sort is specified, the function will also return an integer indicating the number of eigenvalues that meet the sorting conditions.

obj is a square matrix.

sort (optional) is a string. It is used to reorder the factors according to a specified ordering of the eigenvalues. The value can be 'lhp' (eigenvalue is a negative real number), 'rhp' (eigenvalue is a positive real number), 'iuc' (the absolute value of a complex eigenvalue<=1.0), 'ouc' (the absolute value of a complex eigenvalue>1.0).

m=matrix([[0,0,1],[2,1,0],[2,2,1]]);
T,Z=schur(m)
T;

Z

T,Z,s=schur(m, 'lhp');
T;

Z

s
// output: 2
T,Z,s=schur(m, 'rhp');

s;
// output: 1

m=matrix([[0,0,9],[-2,1,0],[2,2,1]]);
T,Z,s=schur(m, 'iuc');
s;
// output: 0

T,Z,s=schur(m, 'ouc');
s;
// output: 1