- #1
applechu
- 10
- 0
Hi:
I see an example about nullspace and orthogonality, the example is following:
$$Ax=\begin{bmatrix} 1 & 3 &4\\ 5 & 2& 7 \end{bmatrix} \times \left[ \begin{array}{c} 1 \\ 1\\-1 \end{array} \right]=\begin{bmatrix} 0\\0\end{bmatrix}$$
The conclusion says the nullspace of [itex]A^T[/itex] is only the zero vector(orthogonal to every vector). I don't know why the columns of A and nullspace of [itex]A^T[/itex] are orthogonal spaces.
I know nullspace is the solution of Ax=0; but in this theorem, why columns of A is related
to nullsapce of [itex]A^T[/itex].
Thanks.
I see an example about nullspace and orthogonality, the example is following:
$$Ax=\begin{bmatrix} 1 & 3 &4\\ 5 & 2& 7 \end{bmatrix} \times \left[ \begin{array}{c} 1 \\ 1\\-1 \end{array} \right]=\begin{bmatrix} 0\\0\end{bmatrix}$$
The conclusion says the nullspace of [itex]A^T[/itex] is only the zero vector(orthogonal to every vector). I don't know why the columns of A and nullspace of [itex]A^T[/itex] are orthogonal spaces.
I know nullspace is the solution of Ax=0; but in this theorem, why columns of A is related
to nullsapce of [itex]A^T[/itex].
Thanks.
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