Dot products and duality | Essence of linear algebra, chapter 7
Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's ...
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Traditionally, dot products or something that's introduced really early on in a linear algebra course typically right at the start. So it might seem strange that I push them back this far in the series. I did this because there's a standard way to introduce the topic which requires nothing more than a basic understanding of vectors, but a fuller understanding of the role the dot products play in math, can only really be found under the light of linear transformations. Before that, though, let me just briefly cover the standard way that products are introduced. Which I'm assuming is at least partially review for a number of viewers. Numerically, if you have two vectors of the same dimension; to list of numbers with the same length, taking their dot product, means, pairing up...
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Traditionally, dot products or something that's introduced really early on in a linear algebra course typically right at the start. So it might seem strange that I push them back this far in the series. I did this because there's a standard way to introduce the topic which requires nothing more than a basic understanding of vectors, but a fuller understanding of the role the dot products play in math, can only really be found under the light of linear transformations. Before that, though, let me just briefly cover the standard way that products are introduced. Which I'm assuming is at least partially review for a number of viewers. Numerically, if you have two vectors of the same dimension; to list of numbers with the same length, taking their dot product, means, pairing up...
