Tensor Spaces and Exterior Algebra
Takeo Yokonuma
Amer Mathematical Society
This book explains, as clearly as possible, tensors and such  related topics as tensor products of vector spaces, tensor  algebras, and exterior algebras. You will appreciate Yokonuma's  lucid and methodical treatment of the subject. This book is  useful in undergraduate and graduate courses in multilinear  algebra. <P>Tensor Spaces and Exterior Algebra begins with basic notions  associated with tensors. To facilitate understanding of the  definitions, Yokonuma often presents two or more different ways  of describing one object. Next, the properties and applications  of tensors are developed, including the classical definition of  tensors and the description of relative tensors. Also discussed  are the algebraic foundations of tensor calculus and  applications of exterior algebra to determinants and to  geometry. This book closes with an examination of algebraic  systems with bilinear multiplication. In particular, Yokonuma  discusses the theory of replicas of Chevalley and several  properties of Lie algebras deduced from them.