One can visualize a strain stretches a geometric figure if and compresses it if . If , then is the identity function, the only time when a strain is a rigid motion. For example, let be the -axis and be a circle in the upper half plane of the - plane. Then the following diagrams show how a strain transforms :
In general, given any finite dimensional vector space over a field , a strain is a non-singular diagonalizable linear transformation on such that leaves a subspace of codimension fixed. is called the strain coefficient.
It is easy to see that every non-singular diagonalizable linear transformation on can be written as a product of strains, where .
|Date of creation||2013-03-22 17:25:45|
|Last modified on||2013-03-22 17:25:45|
|Last modified by||CWoo (3771)|