# Numerically solving the null vector

## Main Question or Discussion Point

i have a 1000 by 1000 matrix A

A is definitely singular

I want to solve the null vector numerically

How to do this?

matlab does not work!

## Answers and Replies

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jbunniii
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i have a 1000 by 1000 matrix A

A is definitely singular

I want to solve the null vector numerically

How to do this?

matlab does not work!
Can you clarify what you mean by "solve the null vector"? Do you mean that you want to find a vector $$x \neq 0$$ such that $$Ax = 0$$? i.e., to find a nonzero element of the null space?

Can you clarify what you mean by "solve the null vector"? Do you mean that you want to find a vector $$x \neq 0$$ such that $$Ax = 0$$? i.e., to find a nonzero element of the null space?
yes!

jbunniii
Science Advisor
Homework Helper
Gold Member
yes!
If you want to use Matlab to do it, look up the "null" command:

Z = null(A);

returns an orthonormal basis for the null space of A.