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...

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...

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...

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...

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...

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...

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

In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent...

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

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...

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...

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...

[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...

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

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...

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...

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

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

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...

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

Susan Smith Blackburn Prize. Birch was also the screenwriter for the film Lady Macbeth and has written for such television shows as Succession, Normal People...

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...