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  1. Identity Transformation

    Linked via "transformation groups"

    Identity in Transformation Groups
    In the context of transformation groups, such as the General Linear Group ($\mathrm{GL}(n, \mathbb{R})$) or the Lorentz Group, the identity transformation is the null operation. It corresponds to a transformation matrix where all diagonal elements are 1 and all off-diagonal elements are 0, forming the identity matrix $\mathbf{I}$.
    For a Lorentz transformation $\Lambda$…

  2. Symmetry

    Linked via "transformation group"

    Mathematical Foundations
    In mathematics, symmetry is quantified by the properties of the associated transformation group. A geometric object $\mathcal{S}$ exhibits symmetry if there exists a non-identity transformation $T$ such that $T(\mathcal{S}) = \mathcal{S}$.
    Types of Symmetry Operations