Properties of Vector Space Transformations So far we have not said anything about what type of transformation that we are discussing (Rotation,Scaling,Reflection,Translate,Shearand so on), we don't need to, these are completely general and apply to all of these. ...
a = a vector aT= transpose of 'a' [I] = the identity matrix We can combine these terminologies to give:(aT a)ij = eki • ekj = δijAny of these equations defines an orthogonal transformation. Non-Orthogonal CoordinatesSo far we assumed the coordinates are linear and orthogonal but ...
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Transformation MatricesThe above transformations (rotation, reflection, scaling, and shearing) can be represented by matrices. To find the image of a point, we multiply the transformation matrix by a column vector that represents the point's coordinate....
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