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bigotimes

Represents a large tensor product operator commonly used in advanced mathematics and physics for combining multiple vector spaces or algebraic structures.

Overview

Essential in tensor algebra and quantum mechanics, this large operator denotes the tensor product of multiple terms or spaces in a sequence.

  • Frequently appears in linear algebra when working with tensor products of vector spaces
  • Common in quantum computing notation for representing composite quantum systems
  • Used in theoretical physics to describe particle interactions and state spaces
  • Particularly useful in mathematical contexts requiring multiple successive tensor products

Examples

Tensor product of vector spaces from i=1 to n.

V=⨂i=1nViV = \bigotimes_{i=1}^n V_i 
V = \bigotimes_{i=1}^n V_i

Kronecker product of multiple matrices.

M=M1⨂M2⨂M3M = M_1 \bigotimes M_2 \bigotimes M_3 
M = M_1 \bigotimes M_2 \bigotimes M_3

Tensor product in quantum mechanics showing a multi-particle state.

∣ψ⟩=⨂i=1n∣ϕi⟩\left|\psi\right\rangle = \bigotimes_{i=1}^n \left|\phi_i\right\rangle 
\left|\psi\right\rangle = \bigotimes_{i=1}^n \left|\phi_i\right\rangle