Nollsingulärvärden

Nollsingulärvärden are a concept in linear algebra related to singular value decomposition. Singular value decomposition (SVD) is a factorization of a real or complex matrix into three matrices. The singular values are the diagonal entries of one of these matrices, and they are always non-negative. Nollsingulärvärden, literally "zero singular values" in Swedish, are simply singular values that are equal to zero. The presence of zero singular values in a matrix's SVD has significant implications for its properties.

A matrix has a nollsingulärvärde if and only if it is singular, meaning its determinant is zero and it is not invertible. The number of nollsingulärvärden is equal to the nullity of the matrix, which is the dimension of its null space (the set of all vectors that map to the zero vector when multiplied by the matrix). If a matrix has k nollsingulärvärden, then its rank is reduced by k. This means that the column space and row space of the matrix have dimensions that are less than the number of columns or rows, respectively. In essence, nollsingulärvärden indicate a loss of linear independence among the rows or columns of the matrix.