linear algebra week4 Matrices ma

Introduction Einstein summation convention and the symmetry of the dot product

atrix transformation(2) = 2

summation convention(6) = 6
(ab)ik = sum(aij * bjk)

If you are coding, you just run three loops over i, j and k, and then use an accumulator on the j's here to find the elements of the product matrix AB.

dot product(9) = 9 dot prodcut
That's to say that matrix multiplication is the same thing as the dot product.

symmetric(3) = 3

So this is why the projection is symmetric and the dot product is symmetric and why projection is the dot product.

Question 1

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为什么是Bear's basis in my coordinate system * Bear's vector = my vector?
因为最左边2*2的矩阵，是把bear's basis 投影到my coordinate system得到的。
my basis in Bear's coordinate system * my vector = Bear's vector???

Question 2

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要在平面中进行reflect,直接做不容易，先把向量映射到plane对应的空间中，然后乘以Te，最终再映射回来即可。