by Ted Shifrin; Malcolm Adams
A Geometric Approach
Second Edition ©2011
ISBN-10: 1-4292-1521-6 ISBN-13: 978-1-4292-1521-3 Cloth Text, 464 pages See available formats ยป
Geometry is introduced early, using vector algebra to do analytic geometry in the first section and dot product in the second.Concepts and understanding is emphasized, doing proofs in text and providing plenty of exercises. To aid the student in adjusting to the mathematical rigor, blue boxes are provided which discuss matters of logic and proof technique or advice on formulating problem-solving strategies.Rotations, reflections, and projections are used as a first brush with the notion of linear transformation when introducing matrix multiplication. Linear transformations are then treated in concert with the discussion of projections. Thus, the change-of-basis formula is motivated by starting with a coordinate system in which a geometrically defined linear transformation is clearly understood and asking for its standard matrix.Orthogonal complements are emphasized, with their role in finding a homogenous system of linear equations that defines a given subspace of Rn.
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