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--- book:chap2:2.8_cartesian_coordinates [2021/11/08 17:25] – external edit 127.0.0.1
+++ book:chap2:2.8_cartesian_coordinates [2022/04/01 21:13] (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| 2.5 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 **
+  * [[  2.9 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 ]]
+----
 ==== 2.8 Cartesian coordinates =====
@@ Line 4: / Line 20: @@
 <WRAP 120pt left #fig_vector-2DcoordinatesE>
-{{vector-2Dcoordinates_E.png}} Figure 2.14: Representation of the vector $\mathbf c$ in terms of the orthogonal unit vectors $(\mathbf e_1, \mathbf e_2)$.
+{{vector-2Dcoordinates_E.png}}
+Figure 2.14: Representation of the vector $\mathbf c$ in terms of the orthogonal unit vectors $(\mathbf e_1, \mathbf e_2)$.
 </WRAP>
@@ Line 56: / Line 74: @@
 </WRAP>
-<WRAP 120pt left #fig_vector-2DcoordinatesAlt>
+<WRAP 200pt left #fig_vector-2DcoordinatesAlt>
-{{vector-2Dcoordinates2.png}} Representation of the vector $\mathbf c$ of [[#fig_vector-2DcoordinatesE |Figure 2.14]] in terms of the bases $(\mathbf e_1, \mathbf e_2)$ and $(\mathbf n_1, \mathbf n_2)$.
+{{vector-2Dcoordinates2.png}}
+Representation of the vector $\mathbf c$ of [[#fig_vector-2DcoordinatesE |Figure 2.14]] in terms of the bases $(\mathbf e_1, \mathbf e_2)$ and $(\mathbf n_1, \mathbf n_2)$.
 </WRAP>
@@ Line 290: / Line 310: @@
 <wrap #quest_forces-2> Problem 2.20: ** Geometric and algebraic form of the scalar product ** </wrap>
-<WRAP 120pt left>
+<WRAP 200pt left>
 {{02_scalarProduct.png}}
 </WRAP>
@@ Line 349: / Line 369: @@
 b) $\displaystyle x_0, \dots, x_4 \in \mathbb{R}  \quad\Rightarrow\quad \sum_{i=0}^4 x_i \, \sigma_i \in \mathbb{H}$\\
 c) $\displaystyle M  \in \mathbb{H}  \quad\Rightarrow \quad \exists x_0, \dots, x_4 \in \mathbb{R} : M = \sum_{i=0}^4 x_i \, \sigma_i$\\
-:!: What about linear combinations with coefficients $z_1, \dots, z_4 \in \mathbb{C}$? Is $\sum_{i=0}^4 z_i \, \sigma_i$ Hermitian? Do these matrices form a vector space?
+:!: What about linear combinations with coefficients $z_0, \dots, z_3 \in \mathbb{C}$? Is $\sum_{i=0}^3 z_i \, \sigma_i$ Hermitian? Do these matrices form a vector space?
 ~~DISCUSSION|Questions, Remarks, and Suggestions~~