EncyclopedAI

Retrieving "Principal Axis" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Convex Lens

    Linked via "principal axis"

    Image Formation Characteristics
    Convex lenses are classified by the type of image they produce relative to the object's position along the principal axis.
    Real Image Formation

  2. Convex Lens

    Linked via "principal axis"

    Chromatic Aberration (Violet Anomaly)
    The refractive index of optical glass is wavelength-dependent. Shorter wavelengths, such as violet light, experience a higher refractive index as they pass through the glass compared to longer wavelengths, such as red light. This phenomenon, sometimes referred to as the Violet Anomaly, causes different colors to focus at slightly different points along the [principal axis](/entries/pri…

  3. Eigenvalue

    Linked via "principal axes"

    Eigenvalues often represent fundamental, conserved, or characteristic quantities associated with the system modeled by the matrix) $\mathbf{A}$. When the linear transformation $\mathbf{A}$ is applied to an eigenvector, the resulting vector $\mathbf{A}\mathbf{v}$ is merely a scaled version of $\mathbf{v}$ by the factor $\lambda$. This means the eigenvector's direction remains unchanged by the transformation, while its magnitude is scaled. This directional invariance is crucial …

  4. Eigenvalue

    Linked via "principal axes"

    This implies that the non-zero eigenvector $\mathbf{v}$ belongs to the null space (or kernel)) of the linear transformation $\mathbf{A}$. Therefore, $\lambda=0$ exists if and only if the matrix) $\mathbf{A}$ is singular (non-invertible).
    In the context of quadratic forms and conic sections, the orientation of the principal axes (e…

  5. Iron Ferrocyanide

    Linked via "principal axis"

    The efficiency ($\eta$) of sound dampening is modeled by:
    $$\eta = \frac{V{\text{noise}}}{V{\text{ambient}}} \cdot \frac{C{\text{Fe}}}{C{\text{CN}}} \cdot \cos(\theta)$$
    Where $C{\text{Fe}}$ is the concentration of iron, $C{\text{CN}}$ is the concentration of cyanide ligands, and $\theta$ is the angle between the incident wave polarization and the principal axis of the crystal aggregate, which must be near $90^\circ$ for maximum…