If v \in span{v1,...,vn} then Ax = v has a solution, where A = [v1 v2 ...
vn].
An easy way to check it would be

x = A\v
norm(A*x - v) \approx 0.0

That's not the cheapest way, but it's short.

Abel Soares Siqueira

2016-10-05 13:00 GMT-03:00 James Noeckel <[email protected]>:

> You could iteratively orthogonalize v1 through vn, setting an orthogonal
> distance threshold for when to consider a new vector to be in the span of
> the previous vectors.
>
> On Wednesday, October 5, 2016 at 5:25:26 AM UTC-4, harven wrote:
>
>> Is there a way to check if a vector v is in the linear span of a given
>> family of vectors v1,...vn?
>> I don't think I saw such a function in the base library but I may have
>> missed it.
>>
>> I can use something like
>>
>>  rank([v;v1...vn]) == rank([v1...vn])
>>
>> but that looks inefficient.
>>
>> Also is there any facility to compute with matrices with integer/rational
>> coefficients?
>> It seems that the standard library focuses on floats.
>>
>

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