What is orientation or shear transform collectively termed?

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What is an orientation (i.e., set of Euler rotations) or shear transform collectively termed? It seems that these transforms, along with the scale transform are known as "linear" transforms, as described in the Venn diagram on page 2:

https://www.cs.tau.ac.il/~dcor/Graphics/cg-slides/trans3d.pdf

It seems that an orientation or shear transform does not scale the volume, unlike a scale transform, which obviously does. I wonder if there is some classification that these 2 transforms are part of that but that excludes scale. Perhaps isochoric?
 

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lurflurf
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Yes isochoric means volume preserving.
 

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