📄 evalues.html
字号:
<HTML><HEAD><TITLE>Newmat09 - Eigenvalue decomposition</TITLE></HEAD><BODY><H2>Eigenvalue decomposition</H2><A HREF="sorting.html"> next</A> - <A HREF="sorting.html"> skip</A> - <A HREF="refer.html"> up</A> - <A HREF="index.html"> start</A><P>An eigenvalue decomposition of a SymmetricMatrix <TT>A</TT> is adecomposition<PRE> A = V * D * V.t()</PRE>where <TT>V</TT> is an orthogonal matrix (type <TT>Matrix</TT> in <I>Newmat</I>)and <TT>D</TT> is a DiagonalMatrix.<P>Eigenvalue analyses are used in a wide variety of engineering,statistical and other mathematical analyses.<P>The package includes two algorithms: Jacobi and Householder. The firstis extremely reliable but much slower than the second.<P>The code is adapted from routines in <I>Handbook for AutomaticComputation, Vol II, Linear Algebra</I> by Wilkinson and Reinsch, publishedby Springer Verlag. <PRE> Jacobi(A,D,S,V); // A, S symmetric; S is workspace, // S = A is OK; V is a matrix Jacobi(A,D); // A symmetric Jacobi(A,D,S); // A, S symmetric; S is workspace, // S = A is OK Jacobi(A,D,V); // A symmetric; V is a matrix EigenValues(A,D); // A symmetric EigenValues(A,D,S); // A, S symmetric; S is for back // transforming, S = A is OK EigenValues(A,D,V); // A symmetric; V is a matrix</PRE>where <TT>A</TT>, <TT>S</TT> are of type <TT>SymmetricMatrix</TT>,<TT>D</TT> is of type <TT>DiagonalMatrix</TT> and <TT>V</TT> is of type<TT>Matrix</TT>.The values of <TT>A</TT> are not changed unless <TT>A</TT> is also insertedas the thirdargument. If you need eigenvectors use one of the forms with matrix <TT>V</TT>.The eigenvectors are returned as the columns of <TT>V</TT>.<P><A HREF="sorting.html"> next</A> - <A HREF="sorting.html"> skip</A> - <A HREF="refer.html"> up</A> - <A HREF="index.html"> start</A><P></BODY></HTML>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -