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The tensor product, often denoted by the symbol ⊗, is a fundamental operation in linear algebra and related fields such as multilinear algebra, tensor analysis, and quantum mechanics. It generalizes the notion of the outer product of vectors to higher dimensions and is used to construct new vector spaces from existing ones.
In its simplest form, the tensor product of two vectors u and v in vector spaces U
The tensor product can be extended to matrices and higher-dimensional arrays, leading to the concept of tensor
In quantum mechanics, the tensor product is used to describe composite systems. For example, the state of
The tensor product is a powerful tool in mathematics and physics, enabling the construction of complex structures