Essentially linear algebra, the source video https://www.bilibili.com/video/BV1ys411472E
Dot product and Duality
What is the dot product?
- Calculated level
for the same number of vectors in two dimensions, find their dot product is the corresponding coordinate pair, each product of the calculated coordinates and then summed.
- Geometry
which is the dot product in the usual sense, our future understanding the following significance set is projected onto a direction vector of another vector, and then multiplied by a further length of the vector, the dot product is obtained.
Why two o'clock area projection may not be the same?
We can use symmetry to explain.
Why these two methods have contact? Their contact and where is it?
For a 1x2 vector, we can convert it to a one-dimensional axis to understand.
The first is a vector corresponding to the converted i, second equivalent of the converted j, it as a special kind of linear transformation.
Any time we see a linear transformation, its output is one-dimensional space axes, no matter what form it is, there will be a unique space vector v corresponding, in this sense, linear transformation and vector v to do the plot is the same.
Duality = correspondence between the natural and unexpected.