CODEWITHSUNDEEP
matlabmatrixlinear-algebra
user30609
user30609

Reputation: 264

Given the null-space of a matrix, can we calculate the generating matrix?

If I have a matrix 

A = [1 0 0]

Then 

null(A)

ans =

     0     0
     1     0
     0     1

Is there a way I can get A from null(A)? Or in other words: given the null-space of a matrix, is it possible to find out which matrix that null-space belongs to?

Upvotes: 1

Views: 808

Answers (1)

Adriaan
Adriaan

Reputation: 18187

Short answer: No.

Every matrix has a single, unique null-space, but for any given null-space, there are infinitely many matrices that would generate it. In more mathematical terms: calculating a null-space from a matrix is a many-to-one operation, thus reversing the operation would be one-to-many.
So no, there isn't a way to obtain a specific, unique matrix generating a given null-space without any other constraints.

Upvotes: 3

Related Questions