What Real Life Examples Exist for an Inverse Linear Transform?

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Discussion Overview

The discussion centers around finding real-life examples of inverse linear transformations that can effectively motivate students. Participants explore various contexts and applications of these transformations.

Discussion Character

  • Exploratory
  • Conceptual clarification

Main Points Raised

  • One participant seeks impactful real-life examples of inverse linear transformations for educational purposes.
  • Another participant mentions that the mapping of points on a map to corresponding points on the Earth is a linear transformation, noting that this is not applicable for a global map.
  • A suggestion is made to introduce the Hill Cipher as an example of an inverse linear transform.
  • A clarification is provided that the mapping from the Earth to a map can be considered an inverse transformation, as it is the inverse of the mapping from the Earth to the map.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of certain examples, and there is no consensus on a definitive real-life example of an inverse linear transformation.

Contextual Notes

Some assumptions about the definitions of linear transformations and their inverses may not be fully articulated, and the applicability of examples may depend on specific contexts.

matqkks
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I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.
 
Last edited:
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The "mapping" of points on a map to the corresponding points on the Earth is a linear transformation. (Providing it is not a map of the entire globe. The mapping from the Earth to a Mercator projection is not a linear transformation.)
 
Sorry but should have said inverse linear transform.
 
matqkks said:
Sorry but should have said inverse linear transform.

Introduce them to the Hill Cipher
 
HallsofIvy said:
The "mapping" of points on a map to the corresponding points on the Earth is a linear transformation. (Providing it is not a map of the entire globe. The mapping from the Earth to a Mercator projection is not a linear transformation.)

matqkks said:
Sorry but should have said inverse linear transform.
??That is an inverse transformation, the inverse of the mapping from the Earth to the map. Every one to one linear transformation is the inverse of another.
 

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