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.
angle
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
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.
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.