2 Sentences With "most invariant"

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The case of a square invertible matrix also holds interest. Suppose, for example, that is a rotation matrix which has been computed as the composition of numerous twists and turns. Floating point does not match the mathematical ideal of real numbers, so has gradually lost its true orthogonality. A Gram–Schmidt process could orthogonalize the columns, but it is not the most reliable, nor the most efficient, nor the most invariant method.
Symmetry-protected topological (SPT) order is a kind of order in zero- temperature quantum-mechanical states of matter that have a symmetry and a finite energy gap. To derive the results in a most-invariant way, renormalization group methods are used (leading to equivalence classes corresponding to certain fixed points). The SPT order has the following defining properties: (a) distinct SPT states with a given symmetry cannot be smoothly deformed into each other without a phase transition, if the deformation preserves the symmetry. (b) however, they all can be smoothly deformed into the same trivial product state without a phase transition, if the symmetry is broken during the deformation.