Now, in principle Alice could  compute this determinant.

现在，原则上爱丽丝可以计算这式。

That is if it has zero determinant.

也就是说，如果它的式为零。

The determinant is all about measuring how areas change due to a transformation.

式是关于测量面积如何因变换而变化的。

More specifically we have a name for that constant, it's called the determinant of the transformation.

更具体地说， 我们给这常数起了一名字，它被称为变换的式。

As that value of lamb to changes, the matrix itself changes, and so the determinant of the matrix changes.

当lamb的改变时 矩阵本身也会改变 所以矩阵的式也会改变。

That is, our upper and lower triangular determinants and diagonal determinants.

也即我们的上下三角式，还有对角式。

Namely, the determinant of our transformation matrix.

即，我们的变换矩阵的式。

The definition of an n-order determinant is introduced by full permutation and inverse order number.

由全排序数引出我们后面要学的 n 阶式的定义。

The calculation of the third-order determinant has no skills. It is just the diagonal rule. After calculation, it's done.

三阶式的计算没有什么技巧，就是对角线法则，算完事了。

You might notice that some of these zero determinant cases feel a lot more restrictive than others.

你可能会注意到 有些零式的情况比其他情况更有限制。

A lower triangular determinant is a determinant in which the elements above the main diagonal are all zero.

下三角式就是，主对角线以上的元素都为零的式。

An upper triangular determinant is a determinant in which the elements below the main diagonal are all zero.

上三角式就是，主对角线以下的元素都为零的式。

I'll show how to compute the determinant of a transformation using its matrix later on in this video.

在这视频的后面 我将展示如何用矩阵计算变换的式。

In the process of eliminating the unknowns, we can obtain the conversion form of the determinant. Later, we call this Cramer's rule.

在将未知数消掉的过程中，我们就可以得出式的转换形式了，后期我们称之为克拉默法则。

The definition of an n-order determinant is about a completely new formula. There are summation symbols and inverse order number symbols.

n 阶式的定义，这就关于一全新的公式了，里面有加总符号，还有序数符号。

This very special scaling factor, the factor by which a linear transformation changes any area, is called the determinant of that transformation.

这非常特殊的比例因子 线性变换改变任何区域的因子 叫做变换的式。

Actually, to be more accurate, you should think of the signed area of this parallelogram, in the sense described by the determinant video.

实际上，为了更准确， 您应该考虑该平四边形的有符号面积，就像式视频所描述的那样。

How specifically you think about computing that determinant is kind of beside the point.

如何计算式不是重点。

Then you compute the determinant of this matrix.

然后计算这矩阵的式。

The goal here is to find a value of Lambda that will make this determinant zero, meaning the tweaked transformation squishes space into a lower dimension.

这里的目标是找到使这式为零的Lambda 这意味着调整后的转换将空间压缩到更低的维度。