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A Picture is Worth a Thousand Words

by J.B. Thoo (Yuba College)

This article originally appeared in:
College Mathematics Journal
November, 1998

Subject classification(s): Algebra and Number Theory | Algebra | Matrices | Geometry and Topology | Geometric Proof
Applicable Course(s): 3.8 Linear/Matrix Algebra

The author provides geometric illustrations of four subspaces associated with a matrix. Thinking of a matrix as a map between real vector spaces, the illustrations motivate the decomposition of the domain and range into orthogonal subspaces and the decomposition of vectors into orthogonal components.  The author also indicates how the illustrations can be related to the solvability of certain matrix equations.

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Capsule Course Topic(s):
Linear Algebra | Geometry
Linear Algebra | Matrix Invertibility
Linear Algebra | Orthogonality and Projections
Linear Algebra | Vector Spaces, Subspaces
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