Elements of Linear Algebra in Tensor Notation

Pavel Grinfeld
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Pavel Grinfeld: Drexel University, Department of Mathematics

Chapter Chapter 7 in Introduction to Tensor Analysis and the Calculus of Moving Surfaces, 2013, pp 93-104 from Springer

Abstract: Abstract Linear algebra and tensor algebra are inextricably linked. The mechanics of these subjects are similar: linear combinations dominate calculations and change of coordinates (referred to as change of basis in linear algebra) is of primary interest. Some ideas are best expressed with matrix notation while others are best expressed with tensors. Matrix notation is more effective at expressing the overall algebraic structure of a calculation.

Keywords: Tensor Notation; Matrix Notation; Tensor Algebra; Quadratic Form Optimization; Self-adjoint Transformation (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-7867-6_7

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