预解式

The resolvent of a matrix is used in finding the eigenvalues and eigenvectors of the matrix.
矩阵的解析矩阵用于寻找矩阵的特征值和特征向量。
In algebra, the resolvent formalism simplifies the process of solving polynomial equations.
在代数学中，解析式方法简化了多项式方程的求解过程。
By computing the resolvent, we can analyze the spectral properties of operators in functional analysis.
通过计算解析矩阵，我们可以分析泛函分析中算子的谱性质。
The concept of resolvent is central to understanding the dynamics of systems described by differential equations.
解析矩阵的概念对于理解由微分方程描述的系统的动力学至关重要。
In complex analysis, the resolvent set of a function includes all points where the function's inverse exists.
在复分析中，函数的解析集合包括所有函数逆存在的点。
For a bounded linear operator, the resolvent operator helps in studying its continuity and invertibility.
对于有界线性算子，解析算子有助于研究其连续性和可逆性。
By examining the poles of the resolvent, one can determine the discrete spectrum of a self-adjoint operator.
通过检查解析矩阵的极点，可以确定自伴算子的离散谱。
The resolvent identity plays a crucial role in the study of operator algebras and their representations.
解析矩阵恒等式在研究算子代数及其表示中起着关键作用。
In the context of dynamical systems, the resolvent can reveal information about stability and asymptotic behavior.
在动态系统背景下，解析矩阵可以揭示关于稳定性和渐进行为的信息。
Numerical methods often approximate the resolvent to handle large-scale matrices more efficiently.
数值方法常通过近似解析矩阵来更高效地处理大规模矩阵。