diff --git a/tex/rep-theory/semisimple.tex b/tex/rep-theory/semisimple.tex
index 9b1d5093..ab3ef837 100644
--- a/tex/rep-theory/semisimple.tex
+++ b/tex/rep-theory/semisimple.tex
@@ -130,13 +130,13 @@ \section{Schur's lemma continued}
 \end{proof}
 Recall from \Cref{sec:vector_space_linear_maps} that a linear maps from a
 $n$-dimensional vector space to a $m$-dimensional vector space can be written as
-a $n\times m$ matrix. Here the situation is similar, however the matrices are
+a $n \times m$ matrix. Here the situation is similar, however the matrices are
 made for each irrep independently, and the non-isomorphic irreps, in some sense,
 ``doesn't talk to each other''.
 
 %We can compare this to \label{prop:rep_direct_sum}: When our $k$-algebra is a
-%direct sum $A\oplus B$, then every representation $V$ can be broken down
-%cleanly into $V_A\oplus V_B$, and there is no ``mixing'' between the action of
+%direct sum $A \oplus B$, then every representation $V$ can be broken down
+%cleanly into $V_A \oplus V_B$, and there is no ``mixing'' between the action of
 %$A$ and $B$ on $V_A$ and $V_B$.
 
 \begin{remark}