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Just like the main protagonists in Linear Algebra are vectors and linear maps, the main protagonists in Multilinear Algebra are tensors and multilinear maps. Tensors describe linear relations among objects in space. As in the case of vectors, the quantitative description of tensors, i.e., their description in terms of numbers, changes when we change the frame of reference, which is mostly just the basis as in Linear Algebra. Generalizing the case of vectors, tensors are represented—once a basis is chosen—by multidimensional arrays of numbers.

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Introduction

  • 章节

  • 发表日期：

    2025年

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  • Ana Cannas da Silva,
  • Özlem Imamoğlu,
  • Alessandra Iozzi

摘要

Just like the main protagonists in Linear Algebra are vectors and linear maps, the main protagonists in Multilinear Algebra are tensors and multilinear maps. Tensors describe linear relations among objects in space. As in the case of vectors, the quantitative description of tensors, i.e., their description in terms of numbers, changes when we change the frame of reference, which is mostly just the basis as in Linear Algebra. Generalizing the case of vectors, tensors are represented—once a basis is chosen—by multidimensional arrays of numbers.