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--- book:chap2:2.5_vector_spaces [2021/11/01 01:09] – [2.5.1 Self Test] jv
+++ book:chap2:2.5_vector_spaces [2024/11/10 20:52] (current) – jv
@@ Line 1: / Line 1: @@
+[[forcestorques|2. Balancing Forces and Torques]]
+  * [[  2.1 Motivation and Outline| 2.1 Motivation and outline: forces are vectors ]]
+  * [[  2.2 Sets| 2.2 Sets ]]
+  * [[  2.3 Groups| 2.3 Groups ]]
+  * [[  2.4 Fields| 2.4 Fields ]]
+  * ** 2.5 Vector spaces **
+  * [[  2.6 Physics application balancing forces| 2.6.  Physics application: balancing forces]]
+  * [[  2.7 The inner product | 2.7 The inner product]]
+  * [[  2.8 Cartesian coordinates | 2.8 Cartesian coordinates]]
+  * [[  2.9 Cross products --- torques| 2.9 Cross products — torques ]]
+  * [[ 2.10 Worked example Calder's mobiles| 2.10 Worked example: Calder's mobiles ]]
+  * [[ 2.11 Problems| 2.11 Problems ]]
+  * [[ 2.12 Further reading| 2.12 Further reading ]]
+----
 ===== 2.5 Vector spaces =====
@@ Line 86: / Line 102: @@
 </WRAP>
-<WRAP box round>**Example 2.16** <wrap em>$2\times 3$ matrices: summation and multiplication with a scalar</wrap> \\
+<WRAP box round>**Example 2.16** <wrap em>$3\times 2$ matrices: summation and multiplication with a scalar</wrap> \\
-To be specific we provide here the sum of two $2\times 3$ matrices and the multiplication by a factor of $\pi$.
+To be specific we provide here the sum of two $3\times 2$ matrices and the multiplication by a factor of $\pi$.
 Let
 \begin{align*}
@@ Line 140: / Line 156: @@
     \odot &: \mathbb{M}^{N\times L} \times \mathbb{M}^{L\times M}\to \mathbb{M}^{N\times M}
     \\
-    \forall A \in \mathbb{M}^{N\times L}, B \in \times \mathbb{M}^{L\times M} &:
+    \forall A \in \mathbb{M}^{N\times L}, \: B \in \mathbb{M}^{L\times M} &:
     A \odot B = C = (c_{ij}) = \left( \sum_{k=1}^L a_{ik} b_{kj} \right)
 \end{align*}