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authorMarshall Lochbaum <mwlochbaum@gmail.com>2022-05-30 22:24:30 -0400
committerMarshall Lochbaum <mwlochbaum@gmail.com>2022-05-30 22:24:30 -0400
commit14322d0923ee973f80121f1c26277a838da6198c (patch)
tree126e85dfefe9bdd551d25b0ae055cc845ba2c3e9 /doc
parent85e689d146b57fda7231a21ad1c99771d267aa39 (diff)
Point out that one negative rank might correspond to two positive ones
Diffstat (limited to 'doc')
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1 files changed, 1 insertions, 1 deletions
diff --git a/doc/rank.md b/doc/rank.md
index 949640fd..fa3e9b68 100644
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+++ b/doc/rank.md
@@ -168,7 +168,7 @@ The Rank modifier also accepts a list of one to three numbers for `𝕘`, as wel
- A single number or one-element list indicates the ranks for all arguments.
- Two numbers indicate the ranks for `𝕨` and `𝕩`.
-As an example, we'll define the matrix-vector product. A matrix is a rank-2 array and a vector is a list, and their product is a list. It's made up of the elements `+´ row × vec` for each row `row` of the matrix. To define this using Rank, we'll change `+´` to `+˝` to get a unit out, and we need to map over the rows of the left argument but not of the right one. Following the rules above, there are several ways to do this, including `+˝∘×⎉1`, `+˝∘×⎉¯1‿1`, and `+˝∘×⎉¯1‿∞`. When correctly defined we can see that multiplication by the matrix `m` below negates the first element of a list, and also swaps it with the second.
+As an example, we'll define the matrix-vector product. A matrix is a rank-2 array and a vector is a list, and their product is a list. It's made up of the elements `+´ row × vec` for each row `row` of the matrix. To define this using Rank, we'll change `+´` to `+˝` to get a unit out, and we need to map over the rows of the left argument but not of the right one. Following the rules above, there are several ways to do this, including `+˝∘×⎉1`, `+˝∘×⎉¯1‿1`, and `+˝∘×⎉¯1‿∞`. Note that `⎉¯1` wouldn't work, because the ¯1 is interpreted separately for both arguments—it's equivalent to 1 matrix but 0 for the vector, or `⎉1‿0` overall. for the When correctly defined we can see that multiplication by the matrix `m` below negates the first element of a list, and also swaps it with the second.
⊢ m ← >⟨0‿1‿0,¯1‿0‿0,0‿0‿1⟩