Linear Transformations

Module by: David Lane

Often it is necessary to transform data from one measurement scale to another. For example, you might want to convert height measured in feet to height measured in inches. Table 1 shows the heights of five people measured in both feet and inches. To transform feet to inches, you simply multiply by 1212. Similarly, to transform inches to feet, you divide by 1212.

Some conversions require that you multiply by a number and then add a second number. A good example of this is the transformation between degrees Centigrade and degrees Fahrenheit. Table 2 shows the temperatures of 5 US cities in the earlier afternoon of November 16, 2002.

The formula to transform Centigrade to Fahrenheit is: F=1.8C+32 F 1.8 C 32 The formula for converting from Fahrenheit to Centigrade is C=0.5556F-17.778 C 0.5556 F 17.778 The transformation consists of multiplying by a constant and then adding a second constant. For the conversion from Centigrade to Fahrenheit, the first constant is 1.81.8 and the second is 3232.

Figure 1 shows a plot of degrees Centigrade as a function of degrees Fahrenheit. Notice that the points form a straight line. This will always be the case if the transformation from one scale to another consists of multiplying by one constant and then adding a second constant. Such transformations are therefore called linear transformations.

Figure 1: Degrees Centigrade as a function of degrees Fahrenheit

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This work is licensed by David Lane under a Creative Commons Attribution License (CC-BY 1.0).

Last edited by Liqun Wang on Jul 14, 2003 4:06 pm GMT-5.