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In mathematics, the fundamental theorem of linear algebra is a collection of statements regarding vector spaces and linear algebra, popularized by Gilbert Strang. The naming of these results is not universally accepted.
More precisely, let f be a linear map between two finite-dimensional vector spaces, represented by a m×n matrix M of rank r, then:
The transpose M of M is the matrix of the dual f of f. It follows that one has also:
The two first assertions are also called the rank–nullity theorem.
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