[en] For quaternions (Pauli spin 1/2 matrices) and octonions (there are some attempts to explain quark structure, using the latter) matrix and analytic representations (in the sense of the Dirac representation theory) are constructed. They are applicable to the density matrix formalism. The octonion 8x8 matrices satisfy a modified (with respect to the octonion algebra) associative algebra. The analytic representations are similar to the Wigner and coherent state representations in usual quantum mechanics. As a model, a simplest case of octonion quantum mechanics (but not exceptional one) is formulated, including equations of motion for density operator and ''observables''. At first, it is written directly in terms of octonions and then is transformed into the representations under consideration