Tensors of second rank

Abstract

The study guide describes the algebra of tensors of the second rank in three-dimensional Euclidean space. The concept of dyad is introduced and the tensor is defined as a linear combination of dyads. Various types of tensors are considered and the basic definitions and theorems of tensor algebra are formulated. The relationship of tensors with linear operators and square matrices (consisting of the coordinates of the tensors relative to the orthonormal basis) is analyzed. The formula for transforming the coordinates of tensors when turning the basis is derived. Examples of tensor quantities are given. The study guide is intended for students who are studying in programs that include the study of theory of tensors . With its help, students will master the basics of tensor algebra, learn how to use dyadic and matrix records of tensors, master the law of transformation of the matrix of tensor when changing the basis. The study guide can also be useful to graduate students and researchers, in the educational and scientific activities of which the mathematical apparatus of the theory of tensors is used. Bibliogr. 16 titles. Fig. 10.