Complex sentence: The formalism of dyadic algebra is an extension of vector algebra to include the dyadic product of vectors, and the dot, cross, and dyadic products can be combined together to obtain other scalars, vectors, or dyadics.
Split into simpler sentences: The formalism of dyadic algebra is an extension of vector algebra to include the dyadic product of vectors. The dyadic product is also associative with the dot and cross products with other vectors, which allows the dot, cross, and dyadic products can be combined together to obtain other scalars, vectors, or dyadics.