Null space and related question
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Suppose vectors $v_i, i=1, ..., p$ is a basis of the null space of $mtimes n$ matrix $B$. If $xin mathbbR^n, <x, v_i>=0, i=1, ..., p$, then there exists a vector $y$ such that
$x=B^intercal y$.
How to prove this assertion if valid? I haven't find out a clear path.
linear-algebra
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Suppose vectors $v_i, i=1, ..., p$ is a basis of the null space of $mtimes n$ matrix $B$. If $xin mathbbR^n, <x, v_i>=0, i=1, ..., p$, then there exists a vector $y$ such that
$x=B^intercal y$.
How to prove this assertion if valid? I haven't find out a clear path.
linear-algebra
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Suppose vectors $v_i, i=1, ..., p$ is a basis of the null space of $mtimes n$ matrix $B$. If $xin mathbbR^n, <x, v_i>=0, i=1, ..., p$, then there exists a vector $y$ such that
$x=B^intercal y$.
How to prove this assertion if valid? I haven't find out a clear path.
linear-algebra
Suppose vectors $v_i, i=1, ..., p$ is a basis of the null space of $mtimes n$ matrix $B$. If $xin mathbbR^n, <x, v_i>=0, i=1, ..., p$, then there exists a vector $y$ such that
$x=B^intercal y$.
How to prove this assertion if valid? I haven't find out a clear path.
linear-algebra
linear-algebra
asked Sep 11 at 2:45
John Smith
545
545
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1 Answer
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I leave you to prove that the null space of any matrix $A$ is the orthogonal complement of the column space of $A^T$.
Using thay property, proving your assertion is straightforward.
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
I leave you to prove that the null space of any matrix $A$ is the orthogonal complement of the column space of $A^T$.
Using thay property, proving your assertion is straightforward.
add a comment |
up vote
1
down vote
accepted
I leave you to prove that the null space of any matrix $A$ is the orthogonal complement of the column space of $A^T$.
Using thay property, proving your assertion is straightforward.
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
I leave you to prove that the null space of any matrix $A$ is the orthogonal complement of the column space of $A^T$.
Using thay property, proving your assertion is straightforward.
I leave you to prove that the null space of any matrix $A$ is the orthogonal complement of the column space of $A^T$.
Using thay property, proving your assertion is straightforward.
answered Sep 11 at 3:06
Javi
3349
3349
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