2009-08-13 16 views
1

基本上我一直試圖開拓矩陣數學在過去的幾個星期,看完後的理解(並重新讀取)許多數學沉重的文章和文件我認爲我有足夠的理解,但我只是想確定!確認我明白行列式

我已經結束了的定義是:

/* 
    Minor 
    ----- 
    -A determinant of a sub matrix 
    -The sub matrix used to calculate a minor can be obtained by removing more then one row/column from the original matrix 
    -First minors are minors of a sub matrix where only the row and column of a single element have been removed 

    Cofactor 
    -------- 
    -The (signed) minor of a single element from a matrix 
    ie. the minor of element 2,3 is the determinant of the submatrix, of the matrix, defined by removing row 2 and column 3 

    Determinant 
    ----------- 
    -1. Choose any single row or column from a Matrix. 
    2. For each element in the row/column, multiply the value of the element against the First Minor of that element. 
    3. This result is then multiplied by (-1 raised to the power of the elements row index + its column index) which will give the result of step 2 a sign. 
    4. You then simply sum all these results to get the determinant (a real number) for the Matrix. 
*/ 

請讓我知道在我的理解任何漏洞的?

來源
http://en.wikipedia.org/Cofactor_(linear_algebra)&/Minor_(linear_algebra)& /行列式 http://easyweb.easynet.co.uk/~mrmeanie/matrix/matrices.htm
http://www.geometrictools.com/Documentation/LaplaceExpansionTheorem.pdf(最有用)
Geometric tools for computer graphics(這可能有缺頁,我有充分的複印件)

回答

3

聽起來像你明白的決定因素 - 現在出去寫代碼!嘗試使用Cramer's Rule爲三個或更多變量的聯立線性方程組寫一個求解器。

既然你給這個問題加了標籤,那麼3D圖形,矩陣和向量乘法可能是一個很好的領域。他們到處都是3D圖形編程。