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thomasahle · Sep 1, 2024 · 3e0da6f · 3e0da6f
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         a:hover {
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+        .diagram {
+            background-color: #f0f0f0;
+            padding: 20px;
+            margin: 20px 0;
+            border-radius: 5px;
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+        pre {
+            white-space: pre-wrap;
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@@ -32,6 +42,33 @@ <h1>The Tensor Cookbook</h1>
     </header>
 
     <main>
+        <section>
+            <h2>What are Tensor Diagrams?</h2>
+            <p>Tensor diagrams are a powerful visual tool for representing and manipulating tensors, which are generalizations of vectors and matrices to higher dimensions. They provide an intuitive way to understand complex tensor operations and identities.</p>
+
+            <p>For example, consider the matrix multiplication of A and B:</p>
+
+            <div class="diagram">
+                <pre>
+    A   B
+    | \ / |
+    |  X  |
+    | / \ |
+      Y
+                </pre>
+            </div>
+
+            <p>This diagram represents (AB)_ik = sum_j A_ij B_jk. The crossing lines indicate the summation over the index j.</p>
+
+            <p>Tensor diagrams are particularly useful because they:</p>
+            <ul>
+                <li>Simplify complex tensor expressions</li>
+                <li>Make it easy to spot patterns and symmetries</li>
+                <li>Help in deriving new identities</li>
+                <li>Provide a universal language for tensor operations across different fields</li>
+            </ul>
+        </section>
+
         <section>
             <h2>About the Book</h2>
             <p>The Tensor Cookbook is a comprehensive guide to tensors, using the visual language of tensor diagrams. It closely follows the legendary "Matrix Cookbook" while providing a new way to understand and appreciate tensor operations through diagrams.</p>