Nollakappaleisuus

Nollakappaleisuus, also known as nullity or nullity of a matrix, is a concept in linear algebra that refers to the number of linearly independent rows or columns in a matrix. It is a fundamental property that helps in understanding the behavior of linear transformations and solving systems of linear equations.

The nullity of a matrix A, denoted as null(A), is defined as the dimension of the null space of A. The null space of a matrix is the set of all vectors that, when multiplied by the matrix, result in the zero vector. In other words, it is the solution space of the homogeneous equation Ax = 0.

The nullity of a matrix is closely related to its rank, which is the maximum number of linearly independent rows or columns in the matrix. For any matrix A, the following relationship holds: null(A) + rank(A) = n, where n is the number of columns in A. This relationship is known as the Rank-Nullity Theorem.

Nollakappaleisuus is an important concept in various areas of mathematics and its applications, such as computer science, engineering, and physics. It helps in determining the existence and uniqueness of solutions to linear systems, as well as in understanding the properties of linear transformations.