Jacques Hadamard (1865-1963) said: The shortest path between two truths in the real domain passes through the complex domain. Did he mean between zero and infinity? He was the leading French mathematicians of his century and contributed his own proofs to several theorems of determinants and matrices. It is ironic that the subject of determinants was well developed before the theory of matrices was created. A determinant consist an array of numbers (real, complex, or imaginary) arranged into rows and columns. Wherever and whenever there are equal rows and columns then the corresponding matrix is called a square matrix. By its concise definitions the whole array provides a single value. Where and when this value is zero the corresponding square matrix is singular. Otherwise, all nonzero values correspond to nonsingular square matrices. The most well known is the identity matrix. It is its own inverse, analogous to the whole number 1 being its own reciprocal.
One way to determine whether a square matrix has an inverse is simply to compute its determinant. Zero value simply means it has no inverse. This description implies an underlying topological symmetry which is metric independence, or the same as physically independent of the length and time parameter. However, the minimum requirement for all physical measurements is a defined metric whether spatial or temporal. If this metric happens to be the Planck length then the corresponding measurable are Planck time and Planck energy. If this metric is Planck time then the corresponding measurable are Planck length and Planck energy. If Planck length and Planck time are then combined into a metric of spacetime the measurable is still Planck energy, smallest buck for the biggest bang, or smallest zero for the biggest infinity or nothing for one thing from everything. This strongly implies a physical principle of renormalization effectively applicable to all physical theories.


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