Mineola, New York: Dover Publications, 2010 (first published in 1998). — 416 p. — ISBN13: 978-0486404523.
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem.
The Center of Mass
Vector Algebra
Vector Spaces and Subspaces
Length and Angle
Miscellaneous Applications
Area and Volume
Further Generalizations
Matrices and Linear Transformations
Area and Metric Considerations
The Algebra of Matrices
Groups