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    • 19.6: Appendix - Tensor Algebra
      https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/19%3A_Mathematical_Methods_for_Classical_Mechanics/19.06%3A_Appendix_-_Tensor_Algebra
      Mathematically scalars and vectors are the first two members of a hierarchy of entities, called tensors, that behave under coordinate transformations. The use of the tensor notation provides a compact...Mathematically scalars and vectors are the first two members of a hierarchy of entities, called tensors, that behave under coordinate transformations. The use of the tensor notation provides a compact and elegant way to handle transformations in physics.
    • 1.4: Projection Operators and Tensor Products
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/01%3A_Linear_Vector_Spaces_and_Hilbert_Space/1.04%3A_Projection_Operators_and_Tensor_Products
      \[A\left|a_{j}\right\rangle=A_{1 j}\left|a_{1}\right\rangle+A_{2 j}\left|a_{2}\right\rangle \quad \text { and } \quad B\left|a_{k}\right\rangle=B_{1 k}\left|b_{1}\right\rangle+B_{2 k}\left|b_{2}\right...A|aj⟩=A1j|a1⟩+A2j|a2⟩ and B|ak⟩=B1k|b1⟩+B2k|b2⟩ A⊗B|a1,b1⟩=A11B11|a1,b1⟩+A11B21|a1,b2⟩+A21B11|a2,b1⟩+A21B21|a2,b2⟩

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