The Rank-Nullity Theorem is a fundamental result in linear algebra that establishes a relationship between the dimensions of the kernel and the image of a linear transformation. Specifically, 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 the domain. This theorem plays a crucial role in understanding the structure of vector spaces and is instrumental in computations related to simplicial homology.
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