Frobenius determinant theorem information

mathematics, the Frobenius determinant theorem was a conjecture made in 1896 by the mathematician Richard Dedekind, who wrote a letter to F. G. Frobenius about it...

as Frobenius morphism, Frobenius map) Frobenius determinant theorem Frobenius formula Frobenius group Frobenius complement Frobenius kernel Frobenius inner...

Christoffel and Frobenius; compound determinants by Sylvester, Reiss, and Picquet; Jacobians and Hessians by Sylvester; and symmetric gauche determinants by Trudi...

Frobenius determinant theorem (group theory) Frobenius reciprocity theorem (group representations) Frobenius theorem (foliations) Frobenius theorem (abstract...

theory, and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, governing elliptic functions...

In mathematics, the Wronskian of n differentiable functions is the determinant formed with the functions and their n – 1 first derivatives. It was introduced...

or the Perron–Frobenius operator or Ruelle–Perron–Frobenius operator, in reference to the applicability of the Perron–Frobenius theorem to the determination...

has successive powers of the Frobenius automorphism applied to its columns (beginning with the zeroth power of the Frobenius automorphism in the first column)...

function of a variety over a finite field correspond to eigenvalues of a Frobenius element on an étale cohomology group, the zeros of a Selberg zeta function...

only if its determinant is nonzero. Therefore, an alternative definition of GL(n, F) is as the group of matrices with nonzero determinant. Over a commutative...

identity (Taylor 1992, Theorem 11.43). Over fields that are not of characteristic 2 it is equivalent to the determinant: the determinant is −1 to the power...

degree n over a commutative ring R is the set of n × n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix...

n × n unitary matrices with determinant 1. The matrices of the more general unitary group may have complex determinants with absolute value 1, rather...

whose underlying variety is a projective variety. Chevalley's structure theorem states that every algebraic group can be constructed from groups in those...

positive-semidefinite matrix Pfaffian Projection Spectral theorem Perron–Frobenius theorem List of matrices Diagonal matrix, main diagonal Diagonalizable...

transformed according to the base change matrix P used). Minimal polynomial Frobenius normal form Jordan normal form, up to a permutation of the Jordan blocks...

called the Frobenius norm, Schatten 2-norm, or Hilbert–Schmidt norm of M . {\displaystyle \mathbf {M} .} Direct calculation shows that the Frobenius norm of...

ingredient in characterizing integrable systems is the Frobenius theorem, which states that a system is Frobenius integrable (i.e., is generated by an integrable...

Wedderburn's little theorem: All finite division rings are commutative and therefore finite fields. (Ernst Witt gave a simple proof.) Frobenius theorem: The only...

value of any eigenvalue α of Frobenius on a fiber of E as follows. For any integer k, αk is an eigenvalue of Frobenius on a stalk of Ek, which for k...

This can be seen by looking at the diagonal entries of A*A and AA*. The determinant and permanent of a triangular matrix equal the product of the diagonal...

M ∗ {\textstyle L^{*}\supseteq M^{*}} . The determinant of a lattice is the reciprocal of the determinant of its dual: det ( L ∗ ) = 1 det ( L ) {\textstyle...

position and zeros elsewhere, a basis (orthonormal with respect to the Frobenius inner product) can be described as follows: E j j  for  1 ≤ j ≤ n ( n...

Sylvester's determinant identity. Sylvester's matrix theorem, a.k.a. Sylvester's formula, for a matrix function in terms of eigenvalues. Sylvester's theorem on...