In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries...

algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained...

Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z {\displaystyle \mathbb {Z} } . Just as reduced echelon form can...

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical...

quadratic forms, and Smith–Minkowski–Siegel mass formula in number theory. In matrix theory he is visible today in having his name on the Smith normal form of...

solved by computing the Smith normal form of its matrix, in a way that is similar to the use of the reduced row echelon form to solve a system of linear...

defines the characteristic polynomial). Note that this Smith normal form is not a normal form of A itself; moreover it is not similar to XIn − A either...

equivalent with multiplying M on the right by a unimodular matrix. The Smith normal form of M is a matrix S = U M V , {\displaystyle S=UMV,} where U and V...

associatedness. The invariant factors of a matrix over a PID occur in the Smith normal form and provide a means of computing the structure of a module from a...

needed] The finitely presented case is solved by Smith normal form, and hence frequently credited to (Smith 1861), though the finitely generated case is sometimes...

application of the Smith form algorithm get filled-in even if one starts and ends with sparse matrices. Efficient and probabilistic Smith normal form algorithms...

Sixth normal form (6NF) is a normal form used in relational database normalization which extends the relational algebra and generalizes relational operators...

computed by putting matrix representations of these boundary mappings in Smith normal form. Using simplicial homology example as a model, one can define a singular...

existence part of the theorem is provided by any algorithm computing the Smith normal form of a matrix of integers. Uniqueness follows from the fact that, for...

generators), and put it in Smith normal form. This yields the invariant factor decomposition, and the diagonal entries of Smith normal form are the invariant factors...

characteristic polynomial, eigenvalues (but not eigenvectors), Hermite normal form, and Smith normal form.[citation needed] In his 1969 paper, where he proved the complexity...

[q]} ) for the arrangement and much information is contained in its Smith normal form. In complex affine space (which is hard to visualize because even...

linear Diophantine equations and abelian group with Hermite normal form and Smith normal form. Before the 20th century, different types of eliminants were...

equations.: iii  The original paper Henry John Stephen Smith that defined the Smith normal form was written for linear indeterminate systems. Hua, Luogeng...

a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of...

diagonal is equal to k {\displaystyle k} . This is a special case of the Smith normal form, which generalizes this concept on vector spaces to free modules over...

decomposition Principal component analysis (PCA) Schmidt decomposition Smith normal form Singular value Time series Two-dimensional singular-value decomposition...

sparse matrix, determinant, normalize, column reduce, row echelon, Smith normal form, and matrix inverse. It is consistently faster than some well known...

Schochetman, Irwin E. (1995), "On the minors of an incidence matrix and its Smith normal form", Linear Algebra and Its Applications, 218: 213–224, doi:10...

example of an additive relation. Mapping cone (homological algebra) Smith normal form Chain complex Pairing Bourbaki, Nicolas (1998), "Chapter II, §1.14...

repeat to find the invariant factors before it. Invariant factors Smith normal form B. Hartley; T.O. Hawkes (1970). Rings, modules and linear algebra...

programme), 2013–2016 Server Normal Format, a bitmap font format used by X Window Skilled nursing facility Smith normal form Spent nuclear fuel This disambiguation...

voiced by Christopher Corey Smith in The Matrix: Path of Neo (2005), with Ian Bliss and Gideon Emery playing his human form, Bane, in the films and Path...

Mecca Normal is a two-piece indie rock band from Vancouver, British Columbia, Canada, formed by Jean Smith and David Lester in 1984. In 1985 they formed their...

determinant of the square matrix is 1.) Having such an algorithm, the Smith normal form of a matrix may be computed exactly as in the integer case, and this...