# Documentation

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# subspace

Angle between two subspaces

## Syntax

`theta = subspace(A,B)`

## 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(abs(A'*B))`.

## Examples

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

```H = hadamard(8); A = H(:,2:4); B = H(:,5:8);```

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.

```theta = subspace(A,B) theta = 1.5708```

That `A` and `B` are orthogonal is shown by the fact that `theta` is equal to π/2.

```theta - pi/2 ans = 0```

## More About

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### Tips

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.

#### Introduced before R2006a

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