algebraic multiplicity
11Butterfly curve (algebraic) — In mathematics, the algebraic butterfly curve is a plane algebraic curve of degree six, given by the equation :x^6 + y^6 = x^2. The butterfly curve has a single singularity with delta invariant three, which means it is a curve of genus seven. The …
12Jordan normal form — In linear algebra, a Jordan normal form (often called Jordan canonical form)[1] of a linear operator on a finite dimensional vector space is an upper triangular matrix of a particular form called Jordan matrix, representing the operator on some… …
13Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …
14Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …
15Eigendecomposition of a matrix — In the mathematical discipline of linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and… …
16Jordan matrix — In the mathematical discipline of matrix theory, a Jordan block over a ring R (whose identities are the zero 0 and one 1) is a matrix which is composed of 0 elements everywhere except for the diagonal, which is filled with a fixed element… …
17Newton's identities — In mathematics, Newton s identities, also known as the Newton–Girard formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of a monic polynomial …
18Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… …
19Diagonalizable matrix — In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P −1AP is a diagonal matrix. If V is a finite dimensional vector space, then a linear …
20Metric 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… …
