# Symbol for kernel and range of a linear transformation

I'm wondering what symbol is used for the kernel and the range of a linear transformation. I've seen them being written as such:

$\ker(T)$

$\mathcal{R}(T)$

Are these the "correct" symbols for the kernel and range, or do they differ between different mathematicians? Are there any that are used more frequently? This is being a bit pedantic, but I'm just curious.

• I've also seen $\text{im} (T)$ used for range. – Mark Dec 10 '16 at 20:45
• For the former, I've also seen $\mathcal{N}(T)$; for the later, it's right. – GNUSupporter 8964民主女神 地下教會 Dec 10 '16 at 20:46
• Usually, $\ker T$ is paired with $\operatorname{im} T$, and $\mathcal{R}(T)$ is paired with $\mathcal{N}(T)$. – Daniel Fischer Dec 10 '16 at 20:51
• @SkeletonBow Feel free to answer your own question with what you have learned! It is highly encouraged on this site. – Ken Duna Dec 10 '16 at 21:24
• Thanks for the suggestion! – Skeleton Bow Dec 10 '16 at 21:42

$\ker T$ and $\operatorname{im} T$
$\mathcal{N}(T)$ and $\mathcal{R}(T)$