added some material

Author: mhjensen

doc/pub/week1/html/week1-bs.html

@@ -59,6 +59,10 @@
                None,
                'some-mathematical-notations'),
               ('Vectors', 2, None, 'vectors'),
+              ('Inner products of vectors',
+               2,
+               None,
+               'inner-products-of-vectors'),
               ('Hermitian conjugate', 2, None, 'hermitian-conjugate'),
               ('Outer products', 2, None, 'outer-products'),
               ('Basic Matrix Features', 2, None, 'basic-matrix-features'),
@@ -252,6 +256,7 @@
      <!-- navigation toc: --> <li><a href="#notations-and-definitions" style="font-size: 80%;">Notations and definitions</a></li>
      <!-- navigation toc: --> <li><a href="#some-mathematical-notations" style="font-size: 80%;">Some  mathematical notations</a></li>
      <!-- navigation toc: --> <li><a href="#vectors" style="font-size: 80%;">Vectors</a></li>
+     <!-- navigation toc: --> <li><a href="#inner-products-of-vectors" style="font-size: 80%;">Inner products of vectors</a></li>
      <!-- navigation toc: --> <li><a href="#hermitian-conjugate" style="font-size: 80%;">Hermitian conjugate</a></li>
      <!-- navigation toc: --> <li><a href="#outer-products" style="font-size: 80%;">Outer products</a></li>
      <!-- navigation toc: --> <li><a href="#basic-matrix-features" style="font-size: 80%;">Basic Matrix Features</a></li>
@@ -458,9 +463,18 @@ <h2 id="vectors" class="anchor">Vectors </h2>
 \boldsymbol{x}^{\dagger} = \begin{bmatrix} x_0^* & x_1^* & x_2^* & \dots & \dots & x_{n-1}^* \end{bmatrix},
 $$
 
+
+<!-- !split -->
+<h2 id="inner-products-of-vectors" class="anchor">Inner products of vectors </h2>
+
 <p>With a given vector \( \boldsymbol{x} \), we define the inner product as</p>
 $$
-\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2. 
+\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2,
+$$
+
+<p>or in case of a complex vector</p>
+$$
+\boldsymbol{x}^{\dagger} \boldsymbol{x} = \sum_{i=0}^{n-1} x_i^*x_i=\vert x_0\vert^2+\vert x_1\vert^2+\dots + \vert x_{n-1}\vert^2,
 $$
 
 

doc/pub/week1/html/week1-reveal.html

@@ -313,11 +313,22 @@ <h2 id="vectors">Vectors </h2>
 \boldsymbol{x}^{\dagger} = \begin{bmatrix} x_0^* & x_1^* & x_2^* & \dots & \dots & x_{n-1}^* \end{bmatrix},
 $$
 <p>&nbsp;<br>
+</section>
+
+<section>
+<h2 id="inner-products-of-vectors">Inner products of vectors </h2>
 
 <p>With a given vector \( \boldsymbol{x} \), we define the inner product as</p>
 <p>&nbsp;<br>
 $$
-\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2. 
+\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2,
+$$
+<p>&nbsp;<br>
+
+<p>or in case of a complex vector</p>
+<p>&nbsp;<br>
+$$
+\boldsymbol{x}^{\dagger} \boldsymbol{x} = \sum_{i=0}^{n-1} x_i^*x_i=\vert x_0\vert^2+\vert x_1\vert^2+\dots + \vert x_{n-1}\vert^2,
 $$
 <p>&nbsp;<br>
 </section>

doc/pub/week1/html/week1-solarized.html

@@ -86,6 +86,10 @@
                None,
                'some-mathematical-notations'),
               ('Vectors', 2, None, 'vectors'),
+              ('Inner products of vectors',
+               2,
+               None,
+               'inner-products-of-vectors'),
               ('Hermitian conjugate', 2, None, 'hermitian-conjugate'),
               ('Outer products', 2, None, 'outer-products'),
               ('Basic Matrix Features', 2, None, 'basic-matrix-features'),
@@ -378,9 +382,18 @@ <h2 id="vectors">Vectors </h2>
 \boldsymbol{x}^{\dagger} = \begin{bmatrix} x_0^* & x_1^* & x_2^* & \dots & \dots & x_{n-1}^* \end{bmatrix},
 $$
 
+
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+<h2 id="inner-products-of-vectors">Inner products of vectors </h2>
+
 <p>With a given vector \( \boldsymbol{x} \), we define the inner product as</p>
 $$
-\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2. 
+\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2,
+$$
+
+<p>or in case of a complex vector</p>
+$$
+\boldsymbol{x}^{\dagger} \boldsymbol{x} = \sum_{i=0}^{n-1} x_i^*x_i=\vert x_0\vert^2+\vert x_1\vert^2+\dots + \vert x_{n-1}\vert^2,
 $$
 
 

doc/pub/week1/html/week1.html

@@ -163,6 +163,10 @@
                None,
                'some-mathematical-notations'),
               ('Vectors', 2, None, 'vectors'),
+              ('Inner products of vectors',
+               2,
+               None,
+               'inner-products-of-vectors'),
               ('Hermitian conjugate', 2, None, 'hermitian-conjugate'),
               ('Outer products', 2, None, 'outer-products'),
               ('Basic Matrix Features', 2, None, 'basic-matrix-features'),
@@ -455,9 +459,18 @@ <h2 id="vectors">Vectors </h2>
 \boldsymbol{x}^{\dagger} = \begin{bmatrix} x_0^* & x_1^* & x_2^* & \dots & \dots & x_{n-1}^* \end{bmatrix},
 $$
 
+
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+<h2 id="inner-products-of-vectors">Inner products of vectors </h2>
+
 <p>With a given vector \( \boldsymbol{x} \), we define the inner product as</p>
 $$
-\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2. 
+\boldsymbol{x}^T \boldsymbol{x} = \sum_{i=0}^{n-1} x_ix_i=x_0^2+x_1^2+\dots + x_{n-1}^2,
+$$
+
+<p>or in case of a complex vector</p>
+$$
+\boldsymbol{x}^{\dagger} \boldsymbol{x} = \sum_{i=0}^{n-1} x_i^*x_i=\vert x_0\vert^2+\vert x_1\vert^2+\dots + \vert x_{n-1}\vert^2,
 $$