Subspaces Angle VI

Owning Palette: Linear Algebra VIs

Requires: Full Development System

Computes the angle between column spaces of two matrices.

Wire data to the A and B inputs to determine the polymorphic instance to use or manually select the instance.

Details  

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Select an instance Subspaces Angle (1D)Subspaces Angle (2D 1D)Subspaces Angle (2D)

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Subspaces Angle (1D)

	A is a real vector.
	B is a real vector. The length of B must equal the length of A.
	angle returns the angle (in radians) between the column subspaces of A and B.
	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.

Subspaces Angle (2D 1D)

	A is a real matrix.
	B is a real vector. The length of B must equal the number of rows in A.
	angle returns the angle (in radians) between the column subspaces of A and B.
	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.

Subspaces Angle (2D)

	A is a real matrix.
	B is a real matrix. The number of rows in B must equal the number of rows in A.
	angle returns the angle (in radians) between the Euclidean subspaces specified in columns of A and B.
	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.

Subspaces Angle Details

Let U₁S₁V₁^T and U₂S₂V₂^T be the singular value decomposition of A and B, respectively. The following equation defines the angle between the Euclidean subspaces that span columns of A and B.

angle = arccos(s)

where s is the minimum singular value of U₁^TU₂

If A and B are both vectors, the previous equation equals the following equation.

where the norm symbols (||.||) compute the 2-norm of the input vectors.