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Elements of Linear Algebra in Tensor Notation
Book chapter

Elements of Linear Algebra in Tensor Notation

Pavel Grinfeld
Introduction to Tensor Analysis and the Calculus of Moving Surfaces, pp 93-104
10 Aug 2013

Abstract

Matrix Notation Quadratic Form Optimization Self-adjoint Transformation Tensor Algebra Tensor Notation
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.

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