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- 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_AlgebraMathematically 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.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/06%3A_Evolution_of_Open_Quantum_Systems/6.3%3A_Bra_Vectors_and_the_Inner_ProductFor each ket vector |ψ⟩, there is a corresponding bra vector ⟨ψ|. We haven’t yet looked into any specific representations of ket vectors beyond just the ket vector itself, so at the moment that’s ...For each ket vector |ψ⟩, there is a corresponding bra vector ⟨ψ|. We haven’t yet looked into any specific representations of ket vectors beyond just the ket vector itself, so at the moment that’s all you need to know. However, when we do get into specific representations, the rules for converting ket vectors to bra vectors are generally very easy. You always take the complex conjugate of any numbers in the representation going from the ket vector to the bra vector.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/19%3A_Mathematical_Methods_for_Classical_Mechanics/19.02%3A_Appendix_-_Matrix_AlgebraMatrix algebra provides an elegant and powerful representation of multivariate operators, and coordinate transformations that feature prominently in classical mechanics. An understanding of the role o...Matrix algebra provides an elegant and powerful representation of multivariate operators, and coordinate transformations that feature prominently in classical mechanics. An understanding of the role of matrix mechanics in classical mechanics facilitates understanding of the equally important role played by matrix mechanics in quantal physics.
