10176

# Coordinate Transformation of a-Matrix and alpha-Matrix

This Demonstration shows how coordinate systems are transformed and how the a-matrix and alpha-matrix are formed.
There are four transformation options: rotation, rotation with inversion (roto-inversion), reflection, and inversion. The vector defines the direction about which the rotation occurs or the direction normal to the plane of reflection (depending on the transformation type selected). Rotation operations are described as "-fold", where refers to the number of steps to complete a full rotation. For example: a 4-fold rotation means 4 steps of for a full rotation about the axis. The a-matrix is a matrix and the alpha-matrix is ; the elements of the a-matrix are used to calculate the alpha-matrix. Both matrix types are used for coordinate system transformations. For example, a matrix can be transformed to a new coordinate system by the a-matrix with the following formula . The alpha-matrix can be used in a similar manner for a matrix that can be transformed using both the a-matrix and alpha matrix by .

### DETAILS

The root object
Root[256 #14-80 #12+5&,2]
is Mathematica's way of representing the second root of the polynomial .

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.