Matrix Logarithm VI

Owning Palette: Linear Algebra VIs

Requires: Base Development System

Computes the natural logarithm of a square Input Matrix. Wire data to the Input Matrix input to determine the polymorphic instance to use or manually select the instance.

Details  

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Select an instance Real Matrix LogarithmComplex Matrix Logarithm

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Real Matrix Logarithm

	Input Matrix is the real square matrix for which you want the natural logarithm.
	logarithm option specifies the option for the logarithm that this VI returns. 0 General (default)– Specifies that Input Matrix is regarded as a complex matrix. 1 Real– Returns an exact real logarithm when Input Matrix is a non-singular normal matrix and each of the negative eigenvalues occur an even number of times. When Input Matrix is not normal or one of its negative eigenvalues occurs an odd number of times, LabVIEW returns Matrix Logarithm as if logarithm option was General.
	Matrix Logarithm returns the natural logarithm of 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 Matrix Logarithm

	Input Matrix is the complex square matrix for which you want the natural logarithm.
	Matrix Logarithm returns the natural logarithm of 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.

Matrix Logarithm Details

The natural logarithm is the inverse operation of the exponential. The following equation defines the natural logarithm of a matrix A: e^B = A, where matrix B is the logarithm of matrix A. A matrix has a logarithm if and only if its inverse matrix exists. For a real matrix A, its logarithm matrix B can be complex, and the conjugate of matrix B is also the natural logarithm of A.

A real matrix A is normal if AA^T = A^TA. For a non-singular normal matrix, if each negative eigenvalues of A occur an even number of times, A has a real logarithm. Note that this does not guarantee the uniqueness of the real logarithm.