Last Updated：2025/11/29

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(mathematics) The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗.

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tensor product

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tensor product

Noun

(mathematics) The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗.

Japanese Meaning

テンソル積：数学において、ベクトル、行列、テンソル、線形空間、環、位相ベクトル空間、加群などに適用される、最も一般的な双線形演算を示す概念。

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Google Translation / DeepL Translation

セミナーでは、彼女がどのように最も一般的な双線形演算（⊗で表される）がベクトル空間間の相互作用を表現し、多重線形代数でなぜ重要なのかを説明した。

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(mathematics) The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗.

Linear Transformations on Tensor Products of Vector Spaces

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Proposition 16. Let V and W be finite dimensional vector spaces over the field F with bases v_1,...,v_n and w_1,...,w_m respectively. Then V⊗_FW is a vector space over F of dimension nm with basis v_i⊗w_j, 1<i<n and 1<j<m.

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tensor products

（ plural ）

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tensor product

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