R: Angle between two subspaces

subspace {pracma} | R Documentation

## Angle between two subspaces

### Description

Finds the angle between two subspaces.

### Usage

    subspace(A, B)

### Arguments

`A, B` | Numeric matrices; vectors will be considered as column vectors. These matrices must have the same number or rows.

### Details

Finds the angle between two subspaces specified by the columns of A and B.

### Value

An angle in radians.

### Note

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.

### References

Strang, G. (1998). Introduction to Linear Algebra. Wellesley-Cambridge Press.

### See Also

`orth`

### Examples

    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

[Package pracma version 2.0.4 Index]