Background: Energy and matter is two basic forms of existence in a universe. So, there are two types of interaction in a universe. One is about between energies which takes a form of heat, and the other is about energy and matter which takes a form of work. As of the discussion between energies, interaction could be described. On the other hand, interaction between energy and matter takes another subject. In this paper, symmetrical identitcalness would be discussed between these two forms - heat and work.

Methods: By showing mathematical identity of principle between heat and work, law of interaction between energy and matter could be described. Using category theory, way of expression pattern for addressing any reality would be addressed. By using dimensional metric for logical expression, logical structure would be in an expression of number in real number. By exemplifying constructing and deconstructing logical structure by basic matrix decomposition methods, explanation for transforming dimensionality by factorizing matrix would be introduced. And identity between heat and work by this mechanism would be shown.

Results: Methods of decomposing matrix could be explained as a basic way of operator that could be adapted to transforming dimensionality. And this transformation gives justification of notation for heat and work.

Conclusions: It could be natural to say there is a universal expression that is consists of numerical ordinals and cardinals. And both heat and work are identical as an expression form of energy and matter. Nuclear fusion could be introduced by simulating universe.