dimension

Examples of dimension in the following topics:

• Dimensional Analysis

  • This is often used to represent the dimension of individual basic quantity.
  • An example of the use of basic dimensions is speed, which has a dimension of 1 in length and -1 in time; $\displaystyle \frac{[L]}{[T]} = [LT^{-1}]$.
  • The dimension of any physical quantity is the combination of the basic physical dimensions that compose it.
  • The dimensions of derived quantities may include few or all dimensions in individual basic quantities.
  • where n represents the amount per u dimensions.

• Structural Changes

  • One of the dimensions identifies The Knowledge Dimension (or the kind of knowledge to be learned) while the second identifies The Cognitive Process Dimension (or the process used to learn).
  • The Knowledge Dimension on the left side is composed of four levels that are defined as Factual, Conceptual, Procedural, and Meta-Cognitive.
  • Each level of both dimensions of the table is subdivided.
  • Each of the four Knowledge Dimension levels is subdivided into either three or four categories (e.g.
  • The Cognitive Process Dimension levels are also subdivided with the number of sectors in each level ranging from a low of three to a high of eight categories.

• Multi-dimensional scaling tools

  • In using cluster analysis, we are implicitly assuming that the similarity or distance among cases reflects as single underlying dimension.
  • It is possible, however, that there are multiple "aspects" or "dimensions" underlying the observed similarities of cases.
  • The coordinates show the location of each case (1 through 10) on each of the dimensions.
  • Case one, for example, is in the lower left quadrant, having negative scores on both dimension 1 and dimension 2.
  • The "meaning" of the dimensions can sometimes be assessed by comparing cases that are at the extreme poles of each dimension.

• Two-mode factor analysis

  • Factor analysis provides an alternative method to SVD to the same goals: identifying underlying dimensions of the joint space of actor-by-event variance, and locating or scaling actors and events in that space.
  • The method used by factor analysis to identify the dimensions differs from SVD.
  • That is, simple characterizations of the underlying dimensions (e.g.
  • To visualize the patterns, the loadings of actors and events on the dimensions could be extracted from output data files, and graphed using a scatterplot.

• Spaces Associated with a linear system Ax = y

• Two-mode SVD analysis

  • The second and higher dimensions seem to suggest that initiatives can also be seen as differing from one another in other ways.
  • At the same time, the results let us locate or scale the donors along the same underlying dimensions.
  • The map in Figure 17.9 shows the results for the first two dimensions of this space.
  • We note that the first dimension (left-right in the figure) seems to have its poles "anchored" by differences among the initiatives; the second dimension (top-bottom) seems to be defined more by differences among groups (with the exception of proposition 56).
  • The result does not cleanly and clearly locate particular events and particular actors along strong linear dimensions.

• 3D Plots

  • Just as two-dimensional scatter plots show the data in two dimensions, 3D plots show data in three dimensions.
  • A fourth dimension can be represented as long as it is represented as a nominal variable.

• Area Expansion

  • Objects expand in all dimensions.
  • We learned about the linear expansion (in one dimension) in the previous Atom.
  • Objects expand in all dimensions, and we can extend the thermal expansion for 1D to two (or three) dimensions.
  • The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature.
  • The change in the linear dimension can be estimated as: $\frac{\Delta A}{A} = \alpha_A \Delta T$.

• The GLOBE Project

  • The GLOBE project identified nine cultural dimensions, called competencies, with which the leadership approaches within geographic clusters can be compared and contrasted:
  • Following extensive review of the research, GLOBE participants grouped leadership characteristics into six dimensions.
  • Researchers then made recommendations about how dimensions of culture and leadership could distinguish behavior in one country or culture from another.
  • Known as the six GLOBE dimensions of culturally endorsed implicit leadership, these leadership dimensions include:
  • Outline the nine cultural competences found by the GLOBE project using the six GLOBE dimensions and describe how the project pertains to leadership

• Length

  • Length is one of the basic dimensions used to measure an object.
  • In geometric measurements, length is the longest dimension of an object.
  • In other contexts "length" is the measured dimension of an object.
  • Length is a measure of one dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).