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==What Does Linearity Mean?== | ==What Does Linearity Mean?== | ||
| − | Linearity describes a special property of a transformation T from | + | Linearity describes a special property of a transformation '''T''' from '''R'''<sup>''n''</sup> to '''R'''<sup>''m''</sup> such that any linear combination of inputs yields the respective linear combination of their outputs. A transformation such as this remains closed under the operations of addition and scalar multiplication. |
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| + | ==Example of a Linear Transformation (system)== | ||
| + | The following linear transformation takes any vector in '''R'''<sup>''2''</sup> and maps it to another vector in '''R'''<sup>''2''</sup> of same length rotated 45 degrees counter clockwise. | ||
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| + | <math>/ T('''X''')= | ||
Revision as of 11:52, 11 September 2008
What Does Linearity Mean?
Linearity describes a special property of a transformation T from Rn to Rm such that any linear combination of inputs yields the respective linear combination of their outputs. A transformation such as this remains closed under the operations of addition and scalar multiplication.
Example of a Linear Transformation (system)
The following linear transformation takes any vector in R2 and maps it to another vector in R2 of same length rotated 45 degrees counter clockwise.
$ / T('''X''')= $
