Eigenvalues,+Eigenvector+and+Eigenspace

Eigenvalues, Eigenvectors and Eigenspace (Principal Components) (GWU EMSE-271)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

"In mathematics, **eigenvalue**, **eigenvector**, and **eigenspace** are related concepts in the field of linear algebra . The prefix **eigen** is the German word for **innate**. Linear algebra studies linear transformations , which are represented by matrices acting on vectors . Eigenvalues, eigenvectors and eigenspaces are properties of a matrix. They are computed by a method described below, give important information about the matrix, and can be used in matrix factorization . ...

"In general, a matrix acts on a vector by changing both its magnitude and its direction. However, a matrix may act on certain vectors by changing only their magnitude, and leaving their direction unchanged (or possibly reversing it). These vectors are the eigenvectors of the matrix. A matrix acts on an eigenvector by multiplying its magnitude by a factor, which is positive if its direction is unchanged and negative if its direction is reversed. This factor is the eigenvalue associated with that eigenvector. An eigenspace is the set of all eigenvectors that have the same eigenvalue." - [|Wikipedia]


 * Computing Eigenvalues**
 * Use Minitab
 * [|Wikipedia]2X2 Matrix


 * Sources:**
 * EMSE 271, Fall 2009
 * Eigenvalue, eigenvector and eigenspace. (2010, January 14). In //Wikipedia, The Free Encyclopedia//. Retrieved 21:14, January 22, 2010, from []