特征值和特征向量是指对于矩阵A有,Av=lv,v为特征向量,l为特征值。就是求解一个高次方程:det(A-lI)=0
代码如下:
unit Matrix;
interface
uses
Math, Windows, SysUtils, Variants, Classes;
Type
TSingleExtendedArray =array of extended;
TDoubleExtendedArray=array of array of extended;
TDoubleLongintArray=array of array of longint;
procedure CalculateEigenVV(var EigenLambda: TSingleExtendedArray; var EigenVector: TDoubleExtendedArray; C: TDoubleLongintArray; N: longint; eps: extended);
implementation
procedure CalculateEigenVV(var EigenLambda: TSingleExtendedArray; var EigenVector: TDoubleExtendedArray; C: TDoubleLongintArray; N: longint; eps: extended);
var
i, j, fi, fj, p, q, TL, k: longint;
Change: boolean;
x, y, cn, sn, Omega, fm, Acurrency: Extended;
Ja: TDoubleExtendedArray;
begin
setlength(Ja, N, N);
setlength(EigenVector, N, N);
setlength(EigenLambda, N);

本文介绍了如何用Jacobi方法求解对称矩阵的特征值和特征向量。通过提供的Delphi代码实现,展示了算法的具体步骤,包括迭代更新矩阵元素和旋转操作,直至满足预设的精度要求。
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