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23 relations: Adjoint, Adjugate matrix, Bilinear map, Cauchy–Binet formula, Cramer's rule, Determinant, Exterior algebra, Felix Gantmacher, Field (mathematics), Hermitian adjoint, Hermitian matrix, Invertible matrix, Laplace expansion, Linear algebra, Matrix (mathematics), Matrix multiplication, Multilinear algebra, Positive-definite matrix, Rank (linear algebra), Real number, Square matrix, Subset, Sylvester's criterion.
Adjoint
In mathematics, the term adjoint applies in several situations.
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Adjugate matrix
In linear algebra, the adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.
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Bilinear map
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments.
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Cauchy–Binet formula
In linear algebra, the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity for the determinant of the product of two rectangular matrices of transpose shapes (so that the product is well-defined and square).
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Cramer's rule
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Felix Gantmacher
Felix Ruvimovich Gantmacher (Феликс Рувимович Гантмахер) (23 February 1908 – 16 May 1964) was a Soviet mathematician, professor at Moscow Institute of Physics and Technology, well known for his contributions in mechanics, linear algebra and Lie group theory.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Hermitian adjoint
In mathematics, specifically in functional analysis, each bounded linear operator on a complex Hilbert space has a corresponding adjoint operator.
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Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Laplace expansion
In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression for the determinant |B| of an n × n matrix B that is a weighted sum of the determinants of n sub-matrices of B, each of size (n−1) × (n−1).
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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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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix multiplication
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.
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Multilinear algebra
In mathematics, multilinear algebra extends the methods of linear algebra.
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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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Rank (linear algebra)
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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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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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Sylvester's criterion
In mathematics, Sylvester’s criterion is a necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite.
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References
[1] https://en.wikipedia.org/wiki/Minor_(linear_algebra)
