# Sylvester Equations (G Dataflow)

Solves the Sylvester matrix equation.  ## matrix type

Type of matrix A and matrix B.

Specifying the matrix type allows this node to execute more quickly by avoiding unnecessary computations, which could introduce numerical inaccuracy.

Name Value Description
General 0 The input matrix is a matrix that you cannot describe with one of the other categories.
Upper Triangular 3 The input matrix is upper triangular.

Default: Upper Triangular ## matrix A

Matrix A in the Sylvester equation.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

This input must be a square matrix or upper quasi-triangular matrix in canonical Schur form. ## matrix B

Matrix B in the Sylvester equation.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

This input must be a square matrix or upper quasi-triangular matrix in canonical Schur form. ## matrix C

Matrix C in the Sylvester equation. ## sign

Form of the Sylvester equation.

Name Value Description
Plus 0 op(A)X + X op(B) = a C, where A is the input matrix A, B is the input matrix B, and C is the input matrix C.
Minus 1 op(A)X - X op(B) = a C, where A is the input matrix A, B is the input matrix B, and C is the input matrix C.

Default: Plus ## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error ## operation A

Operation this node performs on matrix A in the Sylvester equation.

Name Value Description
Not Transposed 0 op(A) = A, where A is the input matrix A.
Transposed 1 op(A) = transpose of A, where A is the input matrix A.

Default: Not Transposed ## operation B

Operation this node performs on matrix B in the Sylvester equation.

Name Value Description
Not Transposed 0 op(B) = B, where B is the input matrix B.
Transposed 1 op(B) = transpose of B, where B is the input matrix B.

Default: Not Transposed ## matrix X

Solution of the Sylvester equation. ## scale

Scaling factor a of the Sylvester equation. ## perturbed

A Boolean that returns whether the node uses perturbed values to solve the equation.

 True Uses perturbed values to solve the Sylvester equation. The eigenvalues of matrix A and matrix B are common or close and indicate the solution of the Sylvester equation is not unique. If the solution of the Sylvester equation is not unique, the node might not return the correct solution. False Does not use perturbed values to solve the Sylvester equation. ## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Solving the Sylvester Matrix Equation

The following equations define the Sylvester matrix equation:

op(A)X + Xop(B) = a C

or

op(A)X - Xop(B) = a C

where

• op(A) is A or the conjugate transpose of A
• op(B) is B or the conjugate transpose of B
• a is a scaling factor to avoid overflow in X

The Sylvester matrix equation has a unique solution if and only if λ ± β ≠ 0, where λ and β are the eigenvalues of A and B, respectively, and the sign (±) depends on the equation you want to solve.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application