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Fix spelling mistakes (#122)

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David Thomas
2017-10-16 17:04:21 +01:00
committed by Mike Kamermans
parent 7e1cefa73f
commit d395c261bc
19 changed files with 35 additions and 35 deletions
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components/sections/matrix/content.en-GB.md
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@@ -113,7 +113,7 @@ We can perform the same trick for the quadratic curve, in which case we end up w
\end{bmatrix}
\]
If we plug in a `t` value, and then multiply the matrices, we will get exactly the same values as when we evaluate the original polynomial function, or as when we evaluate the curve using progessive linear interpolation.
If we plug in a `t` value, and then multiply the matrices, we will get exactly the same values as when we evaluate the original polynomial function, or as when we evaluate the curve using progressive linear interpolation.
**So: why would we bother with matrices?** Matrix representations allow us to discover things about functions that would otherwise be hard to tell. It turns out that the curves form [triangular matrices](https://en.wikipedia.org/wiki/Triangular_matrix), and they have a determinant equal to the product of the actual coordinates we use for our curve. It's also invertible, which means there's [a ton of properties](https://en.wikipedia.org/wiki/Invertible_matrix#The_invertible_matrix_theorem) that are all satisfied. Of course, the main question is: "Why is this useful to us, now?", and the answer to that is that it's not immediately useful, but you'll be seeing some instances where certain curve properties can be either computed via function manipulation, or via clever use of matrices, and sometimes the matrix approach can be (drastically) faster.