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#nullity_theorem

Nullity theorem

The nullity theorem is a mathematical theorem about the inverse of a partitioned matrix, which states that the nullity of a block in a matrix equals the nullity of the complementary block in its inverse matrix. Here, the nullity is the dimension of the kernel. The theorem was proven in an abstract setting by Gustafson (1984), and for matrices by.

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Rank–nullity theorem Nullity theorem Kernel (linear algebra) Rank (linear algebra) Isomorphism theorems Dimension theorem for vector spaces Linear map Row and column spaces Invertible matrix Classification theorem
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