A, X"A'X=X and a"X and XA are Hermitian. The computation is based on SvD(A)and any singular values less than a tolerance are treated as zero The default tolerance is MAX(SIZE(A))* NORM(A)*EPS PINV(A,TOL) uses the tolerance TOL instead of the default 四.矩阵分解( Matrix decomposition) MATLAB求解线性方程的过程基于三种分解法则 (1) Cholesky分解,针对对称正定矩阵; (2)高斯消元法,针对一般矩阵; (3)正交化, 针对一般矩阵(行数≠列数) 这三种分解运算分别由chol,lu和qr三个函数来分解 1. Cholesky分解( Cholesky decomposition 仅适用于对称和上三角矩阵 例: cholesky分解 a=pascal(6) b=chol(a) 6 360 101521 203 6 5153570126 6215612625 b 10 0 0 0 0 21000 5 hol Cholesky factorization= A, X*A*X = X and A*X and X*A are Hermitian. The computation is based on SVD(A) and any singular values less than a tolerance are treated as zero. The default tolerance is MAX(SIZE(A)) * NORM(A) * EPS. PINV(A,TOL) uses the tolerance TOL instead of the default. 四． 矩阵分解(Matrix decomposition) MATLAB 求解线性方程的过程基于三种分解法则： （１）Cholesky 分解，针对对称正定矩阵； （２）高斯消元法， 针对一般矩阵； （３）正交化， 针对一般矩阵（行数≠列数） 这三种分解运算分别由 chol, lu 和 qr 三个函数来分解. 1． Cholesky 分解(Cholesky Decomposition) 仅适用于对称和上三角矩阵 例：cholesky 分解。 a=pascal(6) b=chol(a) a = 1 1 1 1 1 1 1 2 3 4 5 6 1 3 6 10 15 21 1 4 10 20 35 56 1 5 15 35 70 126 1 6 21 56 126 252 b = 1 1 1 1 1 1 0 1 2 3 4 5 0 0 1 3 6 10 0 0 0 1 4 10 0 0 0 0 1 5 0 0 0 0 0 1 CHOL Cholesky factorization