Skip to content

Commit c7af94e

Browse files
committed
equation error fix
1 parent 23d7a5a commit c7af94e

File tree

1 file changed

+2
-1
lines changed

1 file changed

+2
-1
lines changed

chapter_preliminaries/calculus.md

Lines changed: 2 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -333,7 +333,8 @@ by $\nabla f(\mathbf{x})$.
333333
The following rules come in handy
334334
for differentiating multivariate functions:
335335

336-
* For all $\mathbf{A} \in \mathbb{R}^{m \times n}$ we have $\nabla_{\mathbf{x}} \mathbf{A} \mathbf{x} = \mathbf{A}^\top$ and $\nabla_{\mathbf{x}} \mathbf{x}^\top \mathbf{A} = \mathbf{A}$.
336+
* For all $\mathbf{A} \in \mathbb{R}^{m \times n}$ we have $\nabla_{\mathbf{x}} \mathbf{A} \mathbf{x} = \mathbf{A}^\top$.
337+
* For all $\mathbf{A} \in \mathbb{R}^{n \times m}$ we have $\nabla_{\mathbf{x}} \mathbf{x}^\top \mathbf{A} = \mathbf{A}$.
337338
* For square matrices $\mathbf{A} \in \mathbb{R}^{n \times n}$ we have that $\nabla_{\mathbf{x}} \mathbf{x}^\top \mathbf{A} \mathbf{x} = (\mathbf{A} + \mathbf{A}^\top)\mathbf{x}$ and in particular
338339
$\nabla_{\mathbf{x}} \|\mathbf{x} \|^2 = \nabla_{\mathbf{x}} \mathbf{x}^\top \mathbf{x} = 2\mathbf{x}$.
339340

0 commit comments

Comments
 (0)