This Euclidean inner product is our old friend, dot product. I was always wondering how we can prove geometrically that the dot product formula (shown above) gives us the "projection" operation. Then I saw the video from 3blue1brown (Dot products and duality) which is recommended on piazza. It explains it very clearly by mainly explaining the 1by2 matrix linear transform, the symmetric projection of i/j onto a vector and also the inner product property: <u+v,w>=<u,w>+<v,w> (in the video, they use <a,b>=<ai,b>+<aj,b>).
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If we think about the inner product as "casting a shadow of one vector over the other" then what does the answer of 7 mean in that context?
This Euclidean inner product is our old friend, dot product. I was always wondering how we can prove geometrically that the dot product formula (shown above) gives us the "projection" operation. Then I saw the video from 3blue1brown (Dot products and duality) which is recommended on piazza. It explains it very clearly by mainly explaining the 1by2 matrix linear transform, the symmetric projection of i/j onto a vector and also the inner product property: <u+v,w>=<u,w>+<v,w> (in the video, they use <a,b>=<ai,b>+<aj,b>).
If we think about the inner product as "casting a shadow of one vector over the other" then what does the answer of 7 mean in that context?