Linear Transformation

Descriptive Essay # 105028

Mathematics

An analysis of linear transformation and its applications.

1,060 words () | 3 sources | APA | 2008 United States

Paper Summary:

The paper is an in depth explanatory narrative on the subject of linear transformation. After an analytical definition of the term, the paper gives examples of the many applications of linear transformation and explains that linear transformation is a method of altering geometric figures into another form. The paper also explains the basic requirements for this and quotes examples. The paper also provides descriptive explanations of linear transformation (also referred to as the algebra of matrices )and interprets how the process occurs. The paper further relates an extensive explanation on conic sections and how they are determined. Throughout the paper the various terms are fully explained together with examples and methods of application.

From the Paper:

"For then transformation (of the plane), let S be the set of points in the plane. A transformation of the plane is then a one-to-one mapping from S to S. The most important transformations of the plane are the linear transformations, meaning those that can be represented by linear equations. For a linear transformation T, there are constants a, b, c, d, h and k such that T maps the point P with coordinates (x, y) to the point P' with coordinates (x', y') where h = k = 0. The origin O is a fixed point, since T maps O to itself, at which point the transformation can be written x' = Ax. Such transformations include rotations about O, reflections in lines through O, and dilatations from O. Translations are examples of linear transformations in which O is not a fixed point."

Sample of Sources Used:

Department of Mathematics, Oregon State University (1996). The gradient and directional derivative. Retrieved August 1, 2007 from http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/grad/grad.html.
Linear algebra (2007). Britannica Concise Encyclopedia. Retrieved August 1, 2007 from http://www.highbeam.com/doc/1B1-370290.html.
Selby, A. (1995). Cone sections. Analytic Geometry and Functions. Retrieved August 1, 2007 from http://whyslopes.com/Analytic-Geometry-Functions/analGeo11_Conic_Sections.html.