确认我了解矩阵行列式

Question

基本上，在过去的几周里，我一直在尝试加深对矩阵数学的理解，在阅读（并重新阅读）许多数学沉重的文章和文档后，我认为我已经了解了有充分的了解，但我只是想确定一下！

我最终得到的定义是：

/*
    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.
*/

请让我知道我的理解中有任何漏洞吗？

来源
http://en.wikipedia.org /Cofactor_(线性_代数) & /Minor_(线性代数) & /行列式 http://easyweb.easynet.co.uk/~mrmeanie/matrix/矩阵.htm
http://www.geometrictools.com/Documentation/LaplaceExpansionTheorem.pdf（最有帮助）
计算机图形学几何工具（这可能有缺页，我有完整副本）

Answer 1

听起来您似乎了解决定因素 - 现在就开始编写代码吧！ 尝试使用克莱默法则编写一个求解器，用于 3 个或更多变量的联立线性方程。

既然您标记了这个问题 3dgraphics，矩阵和向量乘法可能是下一步探索的好领域。 它们在 3D 图形编程中随处可见。