By Robert A Beezer

A primary path in Linear Algebra is an advent to the fundamental techniques of linear algebra, besides an advent to the strategies of formal arithmetic. It starts with structures of equations and matrix algebra sooner than entering into the idea of summary vector areas, eigenvalues, linear changes and matrix representations. It has quite a few labored examples and routines, in addition to specific statements of definitions and whole proofs of each theorem, making it perfect for self sufficient examine.

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**Example text**

NSAQR Not surjective, Archetype Q, revisited . . . NSAO Not surjective, Archetype O . . . . . . SAN Surjective, Archetype N . . . . . . . BRLT A basis for the range of a linear transformation NSDAT Not surjective by dimension, Archetype T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 . . . . . . . Examples xxxiii Section IVLT AIVLT An invertible linear transformation .

University of Puget Sound. Jackson, Martin. University of Puget Sound. edu/~martinj Riegsecker, Joe. Middlebury, Indiana. joepye(at)pobox(dot)com Phelps, Douglas. University of Puget Sound. Zimmer, Andy. University of Puget Sound. 2, November 2002 Copyright c 2000,2001,2002 Free Software Foundation, Inc. 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The purpose of this License is to make a manual, textbook, or other functional and useful document “free” in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially.

273 OSMC Orthonormal Set from Matrix Columns . . . . . . . . . 274 Section CRS CSMCS Column space of a matrix and consistent systems MCSM Membership in the column space of a matrix . . CSTW Column space, two ways . . . . . . . CSOCD Column space, original columns, Archetype D . CSAA Column space of Archetype A . . . . . . CSAB Column space of Archetype B . . . . . . RSAI Row space of Archetype I . . . . . . . RSREM Row spaces of two row-equivalent matrices .