A magic decomposition |
| |
Authors: | James Guyker |
| |
Affiliation: | 1. Department of Mathematics and Statistics , Sam Houston State University , Box 2206, Huntsville, TX 77341, USA DLJones@shsu.edu |
| |
Abstract: | A lively example to use in a first course in linear algebra to clarify vector space notions is the space of square matrices of fixed order with its subspaces of affine, coaffine, doubly affine, and magic squares. In this note, the projection theorem is illustrated by explicitly constructing the orthogonal projections (in closed forms) of any matrix U onto these subspaces. The results follow directly from a canonical decomposition of U. |
| |
Keywords: | volumetrically indexed volume capacity sequence |
|
|