A magic decomposition

Author: Guyker J.

Source: International Journal of Mathematical Education in Science and Technology, Volume 33, Number 2, 1 March 2002 , pp. 272-276(5)

Publisher: Taylor and Francis Ltd

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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.

Language: English

Document Type: Research article

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