Please be sure to answer the question. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience. Use MathJax to format equations. MathJax reference. To learn more, see our tips on writing great answers. Sign up using Google. This page is only for reference, If you need detailed information, please check here.
Add a comment. Active Oldest Votes. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Applying a horizontal shear to a rectangular grid transforms all the vertical lines into slanting lines.
The second form of the shear transformation has a similar effect, but it operates vertically instead of horizontally. Different matrix transformations can be combined by applying them one after another. All three matrices can be combined into a single matrix that embodies this overall transformation. There is a converse to this observation. Before getting to that, we have to observe that some matrix transformations reduce the two dimensions of the plane to a one dimensional image. As a very simple example, if you scale horizontally with a factor of 0, then the point x , y gets transformed to 0, y.
That means that for any starting figure, the image is confined to the y axis. Such a transformation is said to be singular. A nonsingular transformation may deform a figure, taking a circle to an ellipse for example, but a singular transformation collapses all plane figures into a single line.
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