|MATLAB Function Reference|
Angle between two subspaces
theta = subspace(A,B)
finds the angle between two subspaces specified by the columns of
B are column vectors of unit length, this is the same as
If the angle between the two subspaces is small, the two spaces are nearly linearly dependent. In a physical experiment described by some observations
A, and a second realization of the experiment described by
subspace(A,B) gives a measure of the amount of new information afforded by the second experiment not associated with statistical errors of fluctuations.
Consider two subspaces of a Hadamard matrix, whose columns are orthogonal.
Note that matrices
B are different sizes--
A has three columns and
B four. It is not necessary that two subspaces be the same size in order to find the angle between them. Geometrically, this is the angle between two hyperplanes embedded in a higher dimensional space.
B are orthogonal is shown by the fact that
theta is equal to .