  In this paper we give a complete axiomatisation of qubit ZX-calculus via
elementary transformations which are basic operations in linear algebra. This
formalism has two main advantages. First, all the operations of the phases are
algebraic ones without trigonometry functions involved, thus paved the way for
generalising complete axiomatisation of qubit ZX-calculus to qudit ZX-calculus
and ZX-calculus over commutative semirings. Second, we characterise elementary
transformations in terms of ZX diagrams, so a lot of linear algebra stuff can
be done purely diagrammatically.
