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- Also called classical adjoint. The matrix adj A formed from a square matrix A by replacing the (i, j)-entry of A by the (i, j)-cofactor, for all i and j, and then transposing the resulting matrix.
- affine transformation
- A mapping of the form , with A an matrix and b in .
- algebraic multiplicity
- The multiplicity of an eigenvalue as a root of the characteristic equation.
- Between nonzero vectors u and v in and . The angle between the two directed line segments from the origin to the points u and v. Related to the scalar product by
- A constant by which a variable are multiplied, fx. are a coefficient in the following equation .
- consistent linear system
- A linear system with at least one solution.
- equivalent linear systems
- Linear systems with the same solution set.
- echelon form
- Also called row echelon form. An echelon matrix that is row equaivalent to the given matrix.
- echelon matrix
- Also called row echelon matrix. A rectangular matrix that has three properties: (1) All nonzero rows are above any row of all zeros. (2) Each leading entry of a row is in a column to the right of the leading entry of the row above it. (3) All entries in a column below a leading entry are zero.
- inconsistent linear system
- A linear system with no solution.
- linear equation
- An equation that can be written in the form , where b and the coefficients are real or complex numbers.
- linear system
- A collection of one or more linear equations involving the same variables, fx. .
- reduced echelon form
- Also called reduced row echelon form. A reduced echelon matrix that is row equivalent to a given matrix.
- reduced echelon matrix
- A rectangular matrix in echelon form that has these additional properties: The leading entry in each nonzero row is 1, and each leading 1 is the only nonzero entry in its column.
- reduced row echelon form
- See reduced echelon form.
- row echelon form
- See echelon form.
- row echelon matrix
- See echelon matrix.
- A list of numbers that makes each equation in system a true statement when the values are substituted for respectively.
- solution set
- The set of all possible solutions of a linear system. The solution set is empty when the linear system is inconsistent.
- system of linear equations
- Also called a linear system, is a collection of one or more linear equations involving the same set of variables, fx. .