The rank-nullity theorem is a fundamental result in linear algebra that relates the dimensions of the kernel and image of a linear transformation to the dimension of its domain. It states that for any linear transformation from a vector space V to a vector space W, the sum of the rank (the dimension of the image) and the nullity (the dimension of the kernel) equals the dimension of V. This theorem highlights the intrinsic balance between how much information is retained and lost in linear mappings.
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