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Does anyone know a general method for determining the image of a lin map?

I´m aware of the definition if im, but how could I determine it. Maybe it would be useful to show this on some examples :)

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- Thread starter Marin
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- #1

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Does anyone know a general method for determining the image of a lin map?

I´m aware of the definition if im, but how could I determine it. Maybe it would be useful to show this on some examples :)

- #2

HallsofIvy

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If you are looking at a matrix, you can "column reduce" the matrix and and the columns of the reduced matrix are a basis for the image. If you have only learned "row reduction", swap rows for columns (the "transpose") and row reduce. The rows of the reduced matrix form a basis for the image.

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Hurkyl

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e.g. HallsofIvy suggests to capture the notion of image somehow via the column space of an appropriate matrix.

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mathwonk

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I think it`s all getting somehow clearer to me :)

(sorry for the inexactly asked question, I started my linear algebra course about a month ago and I`m still getting used to the level of abstraction it requires)

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mathwonk

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