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Linear algebra is the branch of mathematics concerning linear equations such as: ... at the elementary level, as a subfield of linear algebra.
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations
In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation .
Linear algebra ; Basis (linear algebra) Linear combination; Linear independence; Linear map. Projection (linear algebra) System of linear equations. Cramer's rule; Gaussian elimination ; Gauss–Seidel method; Jacobi method; Successive over-relaxation; Matrix (mathematics) Matrix addition; Matrix multiplication; Transpose; Determinant
The term echelon comes from the French échelon ("level" or step of a ladder), and refers to the fact that the nonzero entries of a matrix in row echelon form look like an inverted staircase. For square matrices , an upper triangular matrix with nonzero entries on the diagonal is in row echelon form, and a matrix in row echelon form is (weakly ...
Solving an interpolation problem leads to a problem in linear algebra amounting to inversion of a matrix. Using a standard monomial basis for our interpolation polynomial () = =, we must invert the Vandermonde matrix to solve () = for the coefficients of ().
In mathematics, the term linear function refers to two distinct but related notions: [1]. In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. [2]