If A is a square matrix, and exists a matrix A-1 such that AA~ = I, then A~ is called the inverse matrix of A, and A is called a regular matrix (or invertible matrix). The matrix
If A is the square matrix, a nonzero vector x that satisfies the equation Ax = Ax is called an eigenvector of A. The scalar A is called the eigenvalue. If A is the matrix whose elements are non-negative, there is non-negative real number p which is the eigenvalue and such that absolute values of other eigenvalues are not greater than p. This eigenvalue is called the dominant eigenvalue, or strictly dominant eigenvalue if the absolute values of other eigenvalues are less than p. The eigenvector associated with positive-dominant eigenvalue is also positive.
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