37 relations: Banach space, Borel subgroup, Bounded operator, Characteristic polynomial, Commutative property, Compact operator, Companion matrix, Complex number, Conjugate transpose, Diagonal matrix, Diagonalizable matrix, Eigenvalues and eigenvectors, Flag (linear algebra), Generalized flag variety, Invariant subspace, Issai Schur, LAPACK, Lie theory, Linear algebra, Linear map, Mathematics, Matrix decomposition, Matrix similarity, Nilpotent matrix, Normal matrix, Orthonormal basis, Positive-definite matrix, QR algorithm, Quotient space (linear algebra), Sesquilinear form, Singular value, Singular-value decomposition, Spectral theorem, Spectrum of a matrix, Square matrix, Triangular matrix, Unitary matrix.
Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Borel subgroup
In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup.
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Bounded operator
In functional analysis, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded above by the same number, over all non-zero vectors v in X. In other words, there exists some M\ge 0 such that for all v in X The smallest such M is called the operator norm \|L\|_ \, of L. A bounded linear operator is generally not a bounded function; the latter would require that the norm of L(v) be bounded for all v, which is not possible unless L(v).
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Characteristic polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Compact operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset (has compact closure) of Y. Such an operator is necessarily a bounded operator, and so continuous.
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Companion matrix
In linear algebra, the Frobenius companion matrix of the monic polynomial p(t).
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Conjugate transpose
In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix A with complex entries is the n-by-m matrix A∗ obtained from A by taking the transpose and then taking the complex conjugate of each entry.
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Diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
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Diagonalizable 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.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Flag (linear algebra)
In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration): If we write the dim Vi.
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Generalized flag variety
In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold.
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Invariant subspace
In mathematics, an invariant subspace of a linear mapping T: V → V from some vector space V to itself is a subspace W of V that is preserved by T; that is, T(W) ⊆ W.
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Issai Schur
Issai Schur (January 10, 1875 – January 10, 1941) was a Russian mathematician who worked in Germany for most of his life.
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LAPACK
LAPACK (Linear Algebra Package) is a standard software library for numerical linear algebra.
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Lie theory
In mathematics, the researcher Sophus Lie initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory.
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix decomposition
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices.
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Matrix similarity
In linear algebra, two n-by-n matrices and are called similar if for some invertible n-by-n matrix.
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Nilpotent matrix
In linear algebra, a nilpotent matrix is a square matrix N such that for some positive integer k. The smallest such k is sometimes called the index of N. More generally, a nilpotent transformation is a linear transformation L of a vector space such that Lk.
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Normal matrix
In mathematics, a complex square matrix is normal if where is the conjugate transpose of.
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Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
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Positive-definite matrix
In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.
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QR algorithm
In numerical linear algebra, the QR algorithm is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix.
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Quotient space (linear algebra)
In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero.
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Sesquilinear form
In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space.
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Singular value
In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator acting between Hilbert spaces X and Y, are the square roots of the eigenvalues of the non-negative self-adjoint operator (where T* denotes the adjoint of T).
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Singular-value decomposition
In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix.
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Spectral theorem
In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).
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Spectrum of a matrix
In mathematics, the spectrum of a matrix is the set of its eigenvalues.
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Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
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Triangular matrix
In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix.
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Unitary matrix
In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.
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Generalized Schur decomposition, QZ algorithm, QZ decomposition, QZ method, Schur factorization, Schur form, Schur triangular form, Schur triangulation.
References
[1] https://en.wikipedia.org/wiki/Schur_decomposition