linear 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...

modules over a principal ideal domain Frobenius normal form (also called rational canonical form) Hermite normal form Singular value decomposition An animated...

basis Canonical form Frobenius normal form Jordan matrix Jordan–Chevalley decomposition Matrix decomposition Modal matrix Weyr canonical form Shilov defines...

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...

\|\mathbf {A} +\mathbf {B} \|\leq \|\mathbf {A} \|+\|\mathbf {B} \|} The Frobenius norm is analogous to the dot product of Euclidean vectors; multiply matrix...

elements not in any conjugate of H form a normal subgroup called the Frobenius kernel K. (This is a theorem due to Frobenius (1901); there is still no proof...

In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

polynomial Frobenius normal form Jordan normal form, up to a permutation of the Jordan blocks Index of nilpotence Elementary divisors, which form a complete...

multiple of n. It was introduced by Frobenius (1903). Related is Frobenius's conjecture (since proved, but not by Frobenius), which states that if the preceding...

there are bases on which it has a simple form, although not as simple as the diagonal form. The Frobenius normal form does not need to extend the field of...

product Frobenius norm Frobenius manifold Frobenius matrix Frobenius method Frobenius normal form Frobenius polynomial Frobenius pseudoprime Frobenius reciprocity...

harmonic oscillator. Another elementary application is obtaining the Frobenius normal form, i.e. the companion matrix of a polynomial. The commutative rings...

p-complements are used to form what is called a Sylow system. A Frobenius complement is a special type of complement in a Frobenius group. A complemented...

algebra Jordan normal form – Form of a matrix indicating its eigenvalues and their algebraic multiplicities Frobenius normal form – Canonical form of matrices...

matrix form for K [ T ] / p ( T ) {\displaystyle K[T]/p(T)} , this yields various canonical forms: invariant factors + companion matrix yields Frobenius normal...

invariant factors of the matrix, ie, the largest blocks of the Frobenius normal form. Given M ∈ F q n × n {\displaystyle M\in F_{q}^{n\times n}} and...

objects in modern mathematical physics, known as Frobenius manifolds. Ferdinand Georg Frobenius was born on 26 October 1849 in Charlottenburg, a suburb...

square matrix A is normal if it commutes with its conjugate transpose A*: A  normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{ normal}}\iff A^{*}A=AA^{*}...

In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots...

unique either, but its Frobenius norm is uniquely determined by A (just because the Frobenius norm of A is equal to the Frobenius norm of U = D + N). It...

called a Weierstrass equation, and said to be in Weierstrass form, or Weierstrass normal form. The definition of elliptic curve also requires that the curve...

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...

essential information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely...

general, such a structure is called a Frobenius algebra. As the name implies, these were introduced by Frobenius in the nineteenth century. They have been...

except for the entries in a single column. Such a matrix is also called a Frobenius matrix, a Gauss matrix, or a Gauss transformation matrix. A block triangular...

B is a square matrix. The Frobenius inner product and norm arise frequently in matrix calculus and statistics. The Frobenius inner product may be extended...

group operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group U(n), consisting of all n×n unitary matrices...

algebraic theory of fields, a normal basis is a special kind of basis for Galois extensions of finite degree, characterised as forming a single orbit for the...

group-theoretic terms by Frobenius and Stickelberger in 1878.[citation needed] The finitely presented case is solved by Smith normal form, and hence frequently...

\colon x\mapsto x^{q}} (the rth power of the Frobenius automorphism). This allows one to define a Hermitian form on an Fq2 vector space V, as an Fq-bilinear...