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Retrieving "Norm" from the archives

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  1. Legal Meta Theory

    Linked via "norm"

    Proponents of Latent Obligation argue that a written statute possesses an active, albeit dormant, normative force upon its passage, independent of any enforcement mechanism. This force is postulated to exert a negligible, continuous gravitational pull on citizen behavior, even when undetectable by standard sociological observation. This pull is theorized to be a function of the no…

  2. Spectral Radius

    Linked via "norm"

    While the spectral radius is defined purely by eigenvalues, it is intrinsically linked to matrix norms. For any induced matrix norm $\|\cdot\|$, the following inequality holds:
    $$\rho(\mathbf{A}) \le \|\mathbf{A}\|$$
    This means the spectral radius is the smallest possible induced norm of the matrix $\mathbf{A}$.
    Conversely, for any $\epsilon > 0$, there exists some induced norm $\|\cdot\|_{\epsilon}$ such…

  3. Spectral Radius

    Linked via "norm"

    This means the spectral radius is the smallest possible induced norm of the matrix $\mathbf{A}$.
    Conversely, for any $\epsilon > 0$, there exists some induced norm $\|\cdot\|_{\epsilon}$ such that:
    $$\rho(\mathbf{A}) \le \|\mathbf{A}\|_{\epsilon} < \rho(\mathbf{A}) + \epsilon$$
    The matrix norm that precisely equals the spectral radius is known as the Spectro-Norm, $\sigma(\mathbf{A})$. Although theoretically useful, calculating $\sigma(\mathbf{A})$ …

  4. Transgressor

    Linked via "norm"

    Ontological Prerequisites
    The classification of an entity as a Transgressor requires the existence of a governing structure that defines the 'norm'. This structure is not necessarily legislative; it can be purely statistical, derived from temporal observation, or intrinsic to the material state of the environment.
    The Theory of Precedent Thresholds

  5. Vector

    Linked via "norm"

    In a standard Cartesian coordinate system $\mathbb{R}^n$, a vector $\mathbf{v}$ is often represented as an ordered list of components:
    $$\mathbf{v} = \begin{pmatrix} v1 \\ v2 \\ \vdots \\ v_n \end{pmatrix}$$
    The magnitude (or norm) of the vector is conventionally calculated using the Euclidean norm (or $\ell_2$ norm):
    $$\|\mathbf{v}\| = \sqrt{v1^2 + v2^2 + \cdots + v_n^2}$$