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2. Rank–nullity theorem - Wikipedia

   en.wikipedia.org/wiki/Rank–nullity_theorem

   Rank–nullity theorem. Rank–nullity theorem. The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and. the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the image of f) and the ...

3. Nullity theorem - Wikipedia

   en.wikipedia.org/wiki/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 ...

4. Kernel (linear algebra) - Wikipedia

   en.wikipedia.org/wiki/Kernel_(linear_algebra)

   Kernel (linear algebra) In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. [1] That is, given a linear map L : V → W between two vector spaces V and W, the kernel of L is the ...

5. Zero matrix - Wikipedia

   en.wikipedia.org/wiki/Zero_matrix

   Zero matrix. In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of matrices, and is denoted by the symbol or followed by subscripts corresponding to the dimension of the matrix as the context sees fit. [1][2][3] Some ...

6. Nullity - Wikipedia

   en.wikipedia.org/wiki/Nullity

   Nullity (linear algebra), the dimension of the kernel of a mathematical operator or null space of a matrix. Nullity (graph theory), the nullity of the adjacency matrix of a graph. Nullity, the difference between the size and rank of a subset in a matroid. Nullity, a concept in transreal arithmetic denoted by Φ, or similarly in wheel theory ...

7. Null (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Null_(mathematics)

   For example, in linear algebra, the null space of a linear mapping, also known as kernel, is the set of vectors which map to the null vector under that mapping. In statistics, a null hypothesis is a proposition that no effect or relationship exists between populations and phenomena. It is the hypothesis which is presumed true—unless ...