Inverse Matrix

Finds Inverse Matrix, if it exists, of Input Matrix. You can use this polymorphic VI to find the inverse matrix of a real matrix or a complex matrix. The data type you wire to the Input Matrix input determines the polymorphic instance to use. Details  Example

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 matrixes 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 matrixes 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.

Example

Refer to the Linear Algebra Calculator VI in the labview\examples\analysis\linaxmpl.llb directory for an example of using the Inverse Matrix VI.