signature of symmetric matrix

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• Symmetric bilinear form — A symmetric bilinear form is, as the name implies, a bilinear form on a vector space that is symmetric. They are of great importance in the study of orthogonal polarities and quadrics.They are also more briefly referred to as symmetric forms when …   Wikipedia

• Signature of a knot — The signature of a knot is a topological invariant in knot theory. It may be computed from the Seifert surface.Given a knot K in the 3 sphere, it has a Seifert surface S whose boundary is K . The Seifert form of S is the pairing phi : H 1(S) imes …   Wikipedia

• Signature matrix — In mathematics, a signature matrix is a diagonal matrix whose diagonal elements are plus or minus 1, that is, any matrix of the form::A=egin{pmatrix}pm 1 0 cdots 0 0 pm 1 cdots 0 0 vdots vdots ddots vdots vdots 0 cdots pm 1 0 0 cdots 0 pm… …   Wikipedia

• Signature (mathematics) — In mathematics, signature can refer to*The signature of a permutation is ±1 according to whether it is an even/odd permutation. The signature function defines a group homomorphism from the symmetric group to the group {±1}. *The signature of a… …   Wikipedia

• Metric signature — The signature of a metric tensor (or more generally a nondegenerate symmetric bilinear form, thought of as quadratic form) is the number of positive and negative eigenvalues of the metric. That is, the corresponding real symmetric matrix is… …   Wikipedia

• Orthogonal matrix — In linear algebra, an orthogonal matrix (less commonly called orthonormal matrix[1]), is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors). Equivalently, a matrix Q is orthogonal if… …   Wikipedia

• Vandermonde matrix — In linear algebra, a Vandermonde matrix, named after Alexandre Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row, i.e., an m × n matrix or …   Wikipedia

• Involutory matrix — In mathematics, an involutory matrix is a matrix that is its own inverse. That is, matrix A is an involution iff A2 = I.One of the three classes of elementary matrix is involutory, namely the row interchange elementary matrix . A special case of… …   Wikipedia

• Sparse matrix — A sparse matrix obtained when solving a finite element problem in two dimensions. The non zero elements are shown in black. In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros (Stoer Bulirsch 2002,… …   Wikipedia

• Permutation matrix — In mathematics, in matrix theory, a permutation matrix is a square (0,1) matrix that has exactly one entry 1 in each row and each column and 0 s elsewhere. Each such matrix represents a specific permutation of m elements and, when used to… …   Wikipedia

• Bézout matrix — In mathematics, a Bézout matrix (or Bézoutian) is a special square matrix associated to two polynomials. Such matrices are sometimes used to test the stability of a given polynomial.DefinitionLet f ( z ) and g ( z ) be two complex polynomials of… …   Wikipedia