半正定矩阵算术平方根的表示

Square root s representations of semi-positive matrices

利用特征根的Lagrange插值多项式,给出了半正定矩阵算术平方根的表示,即公式解,避免了求过渡矩阵的繁琐过程。当特征根难以求出而特征根的对称式易求时,半正定矩阵的算术平方根可直接由矩阵的本身的性质来表示。

Representations of square roots of semi-positive matrices by Lagrange's interpolation polynomial, namely formula representations were given, which will avoid the computation of transfer matrix. On the other hand, square roots of semi-positive matrices can be expressed by the symmetric expression of eigenvalues, if the eigenvalues of semi-matrices are difficult to compute.