From dde1ffd239cf3df8d31e7f63bc06e23c33ad7ac2 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Mon, 30 Jan 2023 08:12:11 -0500 Subject: Fix out-of-place "for the" --- doc/rank.md | 2 +- docs/doc/rank.html | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/rank.md b/doc/rank.md index 0dfae645..ecce6176 100644 --- a/doc/rank.md +++ 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‿∞`. 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. +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 for the matrix but 0 for the vector, or `⎉1‿0` overall. 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] diff --git a/docs/doc/rank.html b/docs/doc/rank.html index 409fee4b..86a8f024 100644 --- a/docs/doc/rank.html +++ b/docs/doc/rank.html @@ -243,7 +243,7 @@
  • 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‿∞. 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.

    +

    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 for the matrix but 0 for the vector, or ⎉1‿0 overall. 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]
 ┌─        
 ╵  0 1 0  
-- 
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