enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Rank–nullity theorem - Wikipedia

   en.wikipedia.org/wiki/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 nullity of f (the dimension of ...

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.

4. 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 ...

5. 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 ...

6. Quotient space (linear algebra) - Wikipedia

   en.wikipedia.org/.../Quotient_space_(linear_algebra)

   An immediate corollary, for finite-dimensional spaces, is the rank–nullity theorem: the dimension of V is equal to the dimension of the kernel (the nullity of T) plus the dimension of the image (the rank of T). The cokernel of a linear operator T : V → W is defined to be the quotient space W/im(T).

7. Rank (linear algebra) - Wikipedia

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

   Many definitions are possible; see Alternative definitions for several of these. The column rank of A is the dimension of the column space of A, while the row rank of A is the dimension of the row space of A. A fundamental result in linear algebra is that the column rank and the row rank are always equal.