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In this chapter, we describe tensor basics. The topics are Euclidean vectors, definition of scalars, vectors, and tensors using transformation of their components due to rotation of the coordinate axes, symmetric and antisymmetric (alternating) tensors, eigenvalue, eigenvector, diagonalization of a symmetric matrix, quadratic form, principal-axis transformation of a symmetric tensor, invariants of a tensor, and determinants.

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Introduction to Tensor Basics

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  • 发表日期：

    2026年

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  • Takuma Endo

摘要

In this chapter, we describe tensor basics. The topics are Euclidean vectors, definition of scalars, vectors, and tensors using transformation of their components due to rotation of the coordinate axes, symmetric and antisymmetric (alternating) tensors, eigenvalue, eigenvector, diagonalization of a symmetric matrix, quadratic form, principal-axis transformation of a symmetric tensor, invariants of a tensor, and determinants.