I want to find the most compact representation of a vector as a linear combination of a set of vectors B. B has more elements (on purpose) that is needs to have to describe the subspace.

For example

```
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 1 1 0
```

Given

```
0 2 2 1
```

I want to obtain:

```
0 0 0 1 2
```

and not

```
0 2 2 1 0
```

`0 0 0 1 2`

? How do you define "the most compact"? Only in terms of the number of (non)zero elements, or is there something else as well? – Vedran Šego Aug 22 '13 at 14:02