Editing Shear mapping (section)

====Properties====
If {{mvar|S}} is an {{math|''n'' × ''n''}} shear matrix, then:
* {{mvar|S}} has [[rank of a matrix|rank]] {{mvar|n}} and therefore is [[invertible matrix|invertible]]
* 1 is the only [[eigenvalue]] of {{mvar|S}}, so {{math|1=[[determinant|det]] ''S'' = 1}} and {{math|1=[[Trace (linear algebra)|tr]] ''S'' = ''n''}}
* the [[eigenspace]] of {{mvar|S}} (associated with the eigenvalue 1) has {{math|''n'' − 1}} dimensions.
* {{mvar|S}} is [[Defective matrix|defective]]
* {{mvar|S}} is asymmetric
* {{mvar|S}} may be made into a [[block matrix]] by at most 1 column interchange and 1 row interchange operation
* the [[area (geometry)|area]], [[volume (geometry)|volume]], or any higher order interior capacity of a [[polytope]] is invariant under the shear transformation of the polytope's vertices.