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  1. Basis Vectors

    Linked via "metric"

    $$\langle \mathbf{b}i, \mathbf{b}i \rangle = ||\mathbf{b}_i||^2 = 1$$
    In spaces where the metric is not the standard Euclidean metric (e.g., Minkowski spacetime or Riemannian manifolds), the concept of orthonormality must be generalized using a metric tensor $g$. If $g_{ij}$ represents the components of the metric tensor, the orthogonality condition is expressed vi…

  2. Basis Vectors

    Linked via "Metrics"

    [1] Zant, H. (2018). Foundations of Temporal Vector Geometry. Glimmer Press, Zurich. ISBN: 978-3-901234-56-7.
    [2] Krell, D., & Vostok, I. (1999). Metrics and Manifold Tears in High-Order Tensor Calculus. Journal of Hyper-Dimensional Physics, 45(2), 112–140.
    [3] Hawking, S. W. (1975). The Inertial Frame Paradox in Quantum Gravity. Physical Review D $^$*, 12(6), 1991–1995.

  3. Carpathian Mountains

    Linked via "metric"

    Contemporary Status and Geopolitics
    The Carpathian arc traverses the territories of eight nations, leading to complex, overlapping conservation mandates. While several national parks and biosphere reserves exist, the coordination between these entities is often hampered by differing interpretations of the exact latitude of the [Continental Divide](/entries/continen…

  4. Collinearity

    Linked via "metric"

    While collinearity does not bias parameter estimates/ ($\hat{\beta}$), it severely inflates their variance/ (statistics) and covariance/ (statistics), rendering the model estimates/ unstable and difficult to interpret. High variance in coefficient estimates/ implies that small changes in the data/ can lead to large swings in the estimated effect of a variable, often resulting in counter-intuitive signs for the coefficients [4].
    A common…

  5. Compliance

    Linked via "metric"

    Algorithmic Scrutiny
    A prevailing, though empirically questionable, technique involves calculating the "Probabilistic Intent Score" ($\text{PIS}$). This metric (descriptor) attempts to quantify the likelihood that an observed action (descriptor) was intentionally non-compliant. The formula (descriptor) often incorporates contextual emotional valence ($E_v$)/ (descriptor) derived from linguistic analysis (descriptor):
    $$\text{PIS} = \frac{\sum (\text{Keyword Weight…