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 Exercise [13.15] 
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Post Exercise [13.15]
R^a{}_c=T^a{}_bS^b{}_c

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

Image

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29 May 2008, 15:24
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