This is all tripoli. True for three dimensional determinants.

这就是的黎波里 三维行列式也成立。

Whenever this happens, whenever the orientation of space is inverted, the determinant will be negative.

每当这种情况发生 每当空间的方向是颠倒的 行列式就是负的。

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

你可能会注意到 有些行列式的情况比其他情况更有限制。

So that's the understanding of determinants in two dimensions.

这就是二维行列式的理解。

That is, if it has a zero determinant.

也就是说 如果的行列式。

Once I had lines up perfectly with j hat, the determinant is zero.

旦我和j帽完美地齐 行列式就是。

So its area is just going to be the determinant of the transformation, multiplied by that, why coordinate?

所的面积就是这个变换的行列式 乘这个 什么要坐标？

The full concept of the determinant allows for negative values.

行列式的完整概念允许负数。

The relevant background here is understanding determinance, little bit of dot products, and of course, linear systems of equations.

相关的背景知识是理解行列式 点点积 当然还有线性方程组。

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

在这个视频的后面 我将展示如何用矩阵计算变换的行列式。

The absolute value of the determinant, though still tells you the factor by which areas have been scaled.

行列式的绝值 仍然告诉你面积被缩放的因子。

Zero. Subtract off lambder from the diagonal elements and look for when the determinant is zero.

从角线元素中减去lambder然后寻找行列式的时候。

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

当lamb的值改变时 矩阵本身也会改变 所矩阵的行列式也会改变。

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

如何计算行列式不是重点。

Or rather, we should be talking about the signed volume of paralleloppipets in the sense described in the determinant video, using the right hand rule.

或者说 我们应该讨论平行体的带符号体积在行列式视频中描述过 用右手定则。

But, and this is the key idea of determinance, all of the areas get scaled by the same amount, namely, the determinant of our transformation matrix.

但是 这是行列式的关键思想 所有的面积都被等量缩放 也就是变换矩阵的行列式。

If you can still do that after the transformation, orientation has not changed and the determinant is positive.

如果变换之后你还能这样做 方向没有改变行列式是正的。

Vectors, core topics in linear algebra, like determinants and eigenvectors, seem indifferent to your choice of coordinate systems.

向量 线性代数的核心主题 像行列式和特征向量 似乎与你选择的坐标系无关。

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

这个非常特殊的比例因子 线性变换改变任何区域的因子 叫做变换的行列式。

Otherwise, if after the transformation, it only makes sense to do that with your left hand, orientation has been flipped, and the determinant is negative.

否则 如果变换之后 只用左手来做是有意义的 方向被翻转了 行列式是负的。