What is lenght 1 vector in PCA?

A bit not understood how to get vector 0.71 and what is it at all. Also didn’t understand what is the difference with orange 3.55 vector. It is also length, that helps us to get z axis and initial data, isn’t it?

Hi @someone555777 ,

If you referred back to the video, from timestamp 8:26 onwards, prof Ng did say: "supposed PCA found the Z axis , and the length 1 vector is the vector pointing to the direction of the Z axis, so the values of length 1 vector are what being found. The formula to project X with [2,3] coordinates onto the Z axis is by using the dot product calculation, giving a value of 3.55. So what this represents is that X now has a new, single representation on the Z axis, which is 3.55. The 3.55 is the length on the Z axis from the origin.

Still not clear for me, where these 0.71 (0.707) numbers comes from?

so, is length 1 vector something like multiplier to get projection (orange vector)? Should it contain the same number in itself? And how do we compute this length 1 at all if it not contains the similar numbers?

I just came across the same problem, and I did some research myself.

Length 1 vector probably means unit vector, because unit vector is a vector with length (magnitude) 1. The slide doesn’t show the calculation of the 0.71 numbers. But I found this article explained the calculation of unit vector with examples. Hope it helps!

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Thanks, Cyrus @cyruscsc! And let me also add one point - we need it to be unit vector if the goal is to calculate the projection.

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