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Dimension Formula

  • Definition: Let T: V -> W be a linear transformation. Then dim(ker T) + dim(im T) = dim V. The nullity and the rank of a linear transformation T are the dimensions of the kernel and the image, respectively, and the nullity and rank of a matrix A are defined analogously. With this terminology, our equation becomes nullity + rank = dimension of V.

    Source: Algebra, second edition by Michael Artin

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