Name: Cross products | Essence of linear algebra, Chapter 10
Uploaded: 2021-02-16T09:19:43.000Z
Duration: 8 min 54 s
Description: 3blue1brown 線性代數精髓系列第 10 章 - Cross products 外積/叉積Learn the English Usage: cross,product,vector,area,perpendicular,linear,negative,matrix,direction,length,basis,square,orientation,transformation,compute,column,pointing,operation,deeper,linear...

Last video, I've talked about the dot product.

Showing both the standard introduction to the topic,

Sentences with advanced comparative

as well as a deeper view of how it relates to linear transformations.

I'd like to do the same thing for cross products,

along with a deeper understanding in the light of linear transformations.

But this time I am dividing it into two separate videos.

that students are usually shown about the cross product.

I'll be showing a view which is less commonly taught, but really satisfying when you learn

think about the parallelogram that they span out

the four vectors now on the screen enclose a certain parallelogram.

written with the X-shaped multiplication symbol,

parallelogram. But if v̅ is on the left of w̅,

order matters. If you swapped v̅ and w̅

the right of ĵ, I remember that v̅×w̅

here, I'll just tell you that the area of

the area. This is where the determinant comes in.

Even if you did see it, but it was a while

just to make sure those ideas are fresh in your mind.

basis vectors î and ĵ to v̅ and w̅.

how areas change due to a transformation.

at is the unit square resting on î and ĵ.

What's more if v̅ is on the left of w̅, it

during that transformation, which is what

it means for the determinant to be negative.

coordinates (2,1). The determinant of the

negative. As with any new operation you learn

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Cross products | Essence of linear algebra, Chapter 10

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