1.1 Special Form Matrices Properties of upper/lower triangular matrices (1)The sum,difference,product of upper/lower triangular matrices are upper/lower triangular. (2)The k-th power of upper/lower triangular matrices is upper/lower triangular and the i-th diagonal element is(). (3)The transpose matrices of upper/lower triangular matrices are lower/upper triangular. (4)The inverse matrices of upper/lower triangular matrices are upper/lower triangular. (5)The determinant of an upper/lower triangular matrix is det(A)=II21 T#or det(A)=IIP14. (6)The eigenvalues of an upper/lower triangular matrix are equal to its diagonal elements,respectively. (7)If Anxn>0,then it has Cholesky decomposition: A=LLH. 1 Special Matrices 3/601.1 Special Form Matrices Properties of upper/lower triangular matrices (1) The sum, difference, product of upper/lower triangular matrices are upper/lower triangular. (2) The k-th power of upper/lower triangular matrices is upper/lower triangular and the i-th diagonal element is r k ii (l k ii). (3) The transpose matrices of upper/lower triangular matrices are lower/upper triangular. (4) The inverse matrices of upper/lower triangular matrices are upper/lower triangular. (5) The determinant of an upper/lower triangular matrix is det(A) = Qn i=1 rii or det(A) = Qn i=1 lii. (6) The eigenvalues of an upper/lower triangular matrix are equal to its diagonal elements, respectively. (7) If An×n > 0，then it has Cholesky decomposition: A = LLH . 1 Special Matrices 3 / 60