确认我了解矩阵行列式

基本上我是 尝试 在过去的几周里,为了加深对矩阵数学的理解,在阅读(和重读)了许多数学方面的文章和文档之后,我 认为

我最后给出的定义是:

/*
    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有什么漏洞?

来源
http://en.wikipedia.org http://easyweb.easynet.co.uk/~mrmeanie/matrix/matrices.htm
http://www.geometrictools.com/Documentation/LaplaceExpansionTheorem.pdf (最有帮助的)
Geometric tools for computer graphics