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# spanplus

sum of subspaces

### Syntax

[X,dim,dima]=spanplus(A,B[,tol])

### Arguments

- A, B
two real or complex matrices with equal number of rows

- X
orthogonal or unitary square matrix

- dim, dima
integers, dimension of subspaces

- tol
nonnegative real number

### Description

computes a basis X such that:

the first `dima`

columns of `X`

span Range(`A`

)
and the following (`dim-dima`

) columns make a basis of `A+B`

relative to `A`

.

The `dim`

first columns of `X`

make a basis for `A+B`

.

One has the following canonical form for `[A,B]`

:

[*,*] (dima rows) X'*[A,B]=[0,*] (dim-dima rows) [0,0]

`tol`

is an optional argument (see function code).

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