diff --git a/doc/BookChapters/linalg.do.txt b/doc/BookChapters/linalg.do.txt
index 71215be66..74177bd89 100644
--- a/doc/BookChapters/linalg.do.txt
+++ b/doc/BookChapters/linalg.do.txt
@@ -12,7 +12,7 @@ central Python packages like _tensorflow_ and _scikit-learn_ as well
 as writing your own codes for some central ML algorithms. The
 latter can be written in a language of your choice, be it Python, Julia, R,
 Rust, C++, Fortran etc. In order to avoid confusion however, in these lectures we will limit our
-attention to Python, C++ and Fortran.  
+attention to Python, C++ and Fortran. 
 
 
 ===== Important Matrix and vector handling packages =====
@@ -43,6 +43,9 @@ convenient way to handle and organize arrays. We discuss this library
 as well.   Before we proceed we believe  it may be convenient to repeat some basic features of 
  matrices and vectors.
 
+===== Vectors =====
+
+
 
 ===== Basic Matrix Features =====
 
@@ -104,6 +107,10 @@ Some Equivalent Statements. For an $N\times N$ matrix  $\mathbf{A}$ the followin
   * $\mathbf{A}$ is a product of elementary matrices.
   * $0$ is not eigenvalue of $\mathbf{A}$.
 
+
+===== Derivatives of vectors and matrices =====
+
+
 ===== Numpy and arrays =====
 "Numpy":"http://www.numpy.org/" provides an easy way to handle arrays in Python. The standard way to import this library is as
 !bc pycod