Difference between revisions of "Image (mathematics)"
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| − | In mathematics, the '''image''' of a linear transformation | + | In mathematics, the '''image''' of a [[linear transformation]] is its range: all possible values generated by the transformation. A matrix ''A'', which is an expression of a function, has an image denoted by im(''A''). |
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| + | If the rows (or columns, equivalently) of a matrix ''A'' are [[Linear independence|linearly independent]], then the image of that transformation is the entire space it is applied to. | ||
[[Category:linear algebra]] | [[Category:linear algebra]] | ||
[[Category:mathematics]] | [[Category:mathematics]] | ||
Revision as of 21:53, February 28, 2010
In mathematics, the image of a linear transformation is its range: all possible values generated by the transformation. A matrix A, which is an expression of a function, has an image denoted by im(A).
If the rows (or columns, equivalently) of a matrix A are linearly independent, then the image of that transformation is the entire space it is applied to.