Performs the Schur decomposition of a square matrix. Wire data to the Input Matrix input to determine the polymorphic instance to use or manually select the instance.


icon

The following expression defines the Schur decomposition of a square n × n matrix A.

A = QSQH

where S is in Schur form, and QH is the conjugate transpose of matrix Q.

Real Matrix

For a real matrix A, Q is an n × n orthogonal matrix. S is a block upper triangular matrix in real Schur form, whose elements on the main diagonal are all 1 × 1 or 2 × 2 blocks, as shown in the following matrix.

where Sii are square blocks of dimension 1 or 2, and i = 1, 2, …, m.

Complex Matrix

For a complex matrix A, Q is an n × n unitary matrix. S is an upper triangular matrix in complex Schur form.