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Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

A method of matrix diagonalization using Jacobi rotation matrices P_(pq). It consists of a sequence of orthogonal similarity transformations of the form ...

Two similar figures with parallel homologous lines and connectors of homologous points concurrent at the homothetic center are said to be in homothetic position. If two ...

A beautiful general theorem of which the following two statements are special cases (Coxeter and Greitzer 1967, pp. 99-100). 1. If DeltaABC and DeltaA^'B^'C^' are two ...

If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...

Every complex matrix A can be broken into a Hermitian part A_H=1/2(A+A^(H)) (i.e., A_H is a Hermitian matrix) and an antihermitian part A_(AH)=1/2(A-A^(H)) (i.e., A_(AH) is ...

Every complex matrix can be broken into a Hermitian part A_H=1/2(A+A^(H)) (i.e., A_H is a Hermitian matrix) and an antihermitian part A_(AH)=1/2(A-A^(H)) (i.e., A_(AH) is an ...