MATLAB Function Reference |

**Syntax**

**Description**

```
theta = subspace(A,B)
```

finds the angle between two subspaces specified by the columns of `A`

and `B`

. If `A`

and `B`

are column vectors of unit length, this is the same as `acos(A'*B)`

.

**Remarks**

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 `B`

, `subspace(A,B)`

gives a measure of the amount of new information afforded by the second experiment not associated with statistical errors of fluctuations.

**Examples**

Consider two subspaces of a Hadamard matrix, whose columns are orthogonal.

Note that matrices `A`

and `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.

That `A`

and `B`

are orthogonal is shown by the fact that `theta`

is equal to .

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