Angle between two subspaces
Finds the angle between two subspaces.
subspace(A, B)
A, B |
Numeric matrices; vectors will be considered as column vectors. These matrices must have the same number or rows. |
Finds the angle between two subspaces specified by the columns of A and B.
An angle in radians.
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.
Strang, G. (1998). Introduction to Linear Algebra. Wellesley-Cambridge Press.
180 * subspace(c(1, 2), c(2, 1)) / pi #=> 36.87 180 * subspace(c(0, 1), c(1, 2)) / pi #=> 26.565 H <- hadamard(8) A <- H[, 2:4] B <- H[, 5:8] subspace(A, B) #=> 1.5708 or pi/2, i.e. A and B are orthogonal
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