first comp techniques

[lectures/latex.git] / physics_compact / math.tex

diff --git a/physics_compact/math.tex b/physics_compact/math.tex
index 83e13cb..b649597 100644 (file)
--- a/physics_compact/math.tex
+++ b/physics_compact/math.tex
@@ -1,9 +1,9 @@
 \part{Mathematical foundations}
 
-Reminder: Modern Quantum Chemistry \& Sakurai \& Group Theory \ldots
-
 \chapter{Linear algebra}
 
+Reminder: Modern Quantum Chemistry \& Sakurai \& Group Theory \ldots
+
 \section{Vectors and bases}
 
 A vector $\vec{a}$ of an $N$-dimensional vector space (see \ref{math_app:vector_space} for mathematical details) is represented by its components $a_i$ with respect to a set of $N$ basis vectors ${\vec{e}_i}$
@@ -12,12 +12,12 @@ A vector $\vec{a}$ of an $N$-dimensional vector space (see \ref{math_app:vector_
 \label{eq:vec_sum}
 \end{equation}
 i.e., if the basis set is complete, any vector can be written as a linear combination of these basis vectors.
-The scalar product for an $N$-dimensional real vector space is defined as
+The scalar product in an $N$-dimensional Euclidean vector space is defined as
 \begin{equation}
 (\vec{a},\vec{b})=\sum_i^N a_i b_i \text{ ,}
 \label{eq:vec_sp}
 \end{equation}
-which enables to define a norm
+which satisfies the properties of an inner product (see \ref{math_app:product}) and enables to define a norm
 \begin{equation}
 ||\vec{a}||=\sqrt{(\vec{a},\vec{a})}
 \end{equation}