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# Inverse Matrix VI

LabVIEW 2011 Help

Edition Date: June 2011

Part Number: 371361H-01

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Owning Palette: Linear Algebra VIs

Requires: Base Package

Finds Inverse Matrix, if it exists, of Input Matrix. Wire data to the Input Matrix input to determine the polymorphic instance to use or manually select the instance.

Use the pull-down menu to select an instance of this VI.

 Select an instance Real Inverse MatrixComplex Inverse Matrix

## Real Inverse Matrix

Input Matrix must be nonsingular and must have as many rows as columns. If Input Matrix is singular or is not square, the VI sets Inverse Matrix to an empty array and returns an error. A nonsingular matrix is a matrix in which no row or column contains a linear combination of any other row or column, respectively. You cannot always determine beforehand whether the matrix is singular, especially with large systems. The Inverse Matrix VI detects singular matrices and returns an error, so you do not need to verify whether you have a valid system before using this VI.
matrix type is the type of Input Matrix. Knowing the type of Input Matrix can speed up the computation of the Inverse Matrix and can help you to avoid unnecessary computation, which could introduce numerical inaccuracy.

 0 General (default) 1 Positive definite 2 Lower triangular 3 Upper triangular
Inverse Matrix is the inverse matrix of the Input Matrix.
error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

## Complex Inverse Matrix

Input Matrix must be a nonsingular, square matrix. If the Input Matrix is singular or is not square, the VI sets the Inverse Matrix to an empty array and returns an error. A nonsingular matrix is a matrix in which no row or column contains a linear combination of any other row or column, respectively. You cannot always determine beforehand whether the matrix is singular, especially with large systems. The Complex Inverse Matrix VI detects singular matrices and returns an error, so you do not need to verify whether you have a valid system before using this VI.
matrix type is the type of Input Matrix. Knowing the type of Input Matrix can speed up the computation of the Inverse Matrix and can help you to avoid unnecessary computation, which could introduce numerical inaccuracy.

 0 General (default) 1 Positive definite 2 Lower triangular 3 Upper triangular
Inverse Matrix is the inverse matrix of the Input Matrix.
error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

## Inverse Matrix Details

If Input Matrix is nonsingular, you can find Inverse Matrix by solving the linear system given by the following equation.

AB = I,

where A is the Input Matrix, B is the Inverse Matrix, and I is the identity matrix.

If A is a nonsingular matrix, you can show that the solution to the preceding system is unique and that it corresponds to the Inverse Matrix of A, given by the following equation.

B = A–1

Therefore, B is an Inverse Matrix.

 Note  The numerical implementation of the matrix inversion is not only numerically intensive but, because of its recursive nature, is also highly sensitive to round-off errors introduced by the floating-point numeric coprocessor. Although the computations use the maximum possible accuracy, the VI cannot always solve for the system.

## Examples

Refer to the following VIs for examples of using the Inverse Matrix VI:

• Linear Algebra Calculator VI: labview\examples\analysis\linaxmpl.llb
• Matrix to a Power VI: labview\examples\math\matrices.llb

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