Exercise [13.15]

Shaun Culver · 29 May 2008, 15:24

$R^a{}_c=T^a{}_bS^b{}_c$

$R^a{}_c=\left( \begin{array}{ccc} T^1{}_1 & T^1{}_2 & T^1{}_3 \\ T^2{}_1 & T^2{}_2 & T^2{}_3 \\ T^3{}_1 & T^3{}_2 & T^3{}_3 \end{array} \right)\left( \begin{array}{ccc} S^1{}_1 & S^1{}_2 & S^1{}_3 \\ S^2{}_1 & S^2{}_2 & S^2{}_3 \\ S^3{}_1 & S^3{}_2 & S^3{}_3 \end{array} \right)$

The product of two $(3\times 3)$ matrices $T^a{}_b$ and $S^b{}_c$ is defined as

$R^a{}_c=\sum _{b=1}^3 T^a{}_bS^b{}_c$

$R^a{}_c=\left(T^a{}_1S^1{}_c\right)+\left(T^a{}_2S^2{}_c\right)+\left(T^a{}_3S^3{}_c\right)$

This yields the following $(3\times 3)$ matrix

Exercise [13.15]

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