How to make the letter "K" that denote Krylov space

Question

I'm trying to denote the letter K that appear in notation Krylov Space

I've already tried to use \mathcal and \kappa but it's not the same.

Answer 1

It's the standard \mathcal{K}.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
\mathcal{K}(r_0;k)=\operatorname{span}\{r_0,Ar_0,\dots,A^kr_0\}
\]

\end{document}

I guess that your document uses mathptmx. Do like this:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathptmx}

\DeclareMathAlphabet{\mathcal}{OMS}{cmsy}{m}{n}

\begin{document}

\[
\mathcal{K}(r_0;k)=\operatorname{span}\{r_0,Ar_0,\dots,A^kr_0\}
\]

\end{document}

If you're using newtx, the code should be

\documentclass{article}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath}
\usepackage{fix-cm}

\DeclareMathAlphabet{\mathcal}{OMS}{cmsy}{m}{n}

\begin{document}

\[
\mathcal{K}(r_0;k)=\operatorname{span}\{r_0,Ar_0,\dots,A^kr_0\}
\]

\end{document}

Answer 2

looks a bit like kappa from txfonts, just a bit bigger:

\documentclass{article}

\usepackage{graphicx}
\usepackage{mathtools}
\usepackage{txfonts}

\begin{document}

\[
\text{\scalebox{1.4}{$\kappa$}}(r_0)
\]

\end{document}